Define the term equilibrium position in simple harmonic motion.

The term equilibrium position in simple harmonic motion is the position where there is no resultant force acting on an object.

What does displacement mean in oscillations?

Displacement in oscillations is the horizontal or vertical distance of a point on the wave from its equilibrium position.

True or False? The period of an oscillation is measured in seconds.

True. The period of an oscillation is measured in seconds (s).

What is the amplitude of an oscillation?

The amplitude of an oscillation is the maximum value of the displacement on either side of the equilibrium position.

State the meaning of frequency in terms of oscillations.

Frequency is the number of oscillations per second and it is measured in hertz (Hz).

Define angular frequency .

Angular frequency is the change of angular displacement with respect to time and is measured in radians per second (rad s −1 ).

What is simple harmonic motion (SHM)?

Simple harmonic motion (SHM) is a type of oscillation where the restoring force is directly proportional to the displacement and directed towards the equilibrium position.

True or False? In SHM, the time interval of each complete vibration is the same.

True. In SHM, the time interval of each complete vibration, known as the period, is constant.

What are the two properties of the restoring force in simple harmonic motion?

The two properties of the restoring force in simple harmonic motion are that: it is always directed towards the equilibrium position it is proportional to the displacement from the equilibrium position

State one example of an object undergoing SHM.

Examples of objects undergoing SHM are: The pendulum of a clock A child on a swing A rope bridge A marble in a bowl A bowl set vibrating A mass oscillating on a spring A bungee jumper coming to a stop at the end of their fall

How does acceleration relate to displacement in SHM?

In SHM, acceleration is proportional to displacement and in the opposite direction to it.

True or False? The period of oscillation in SHM depends on the amplitude of oscillation.

False. The period of oscillation in SHM is independent of the amplitude for small angles of oscillation.

Define angular frequency in the context of SHM.

Angular frequency in SHM is the change of angular displacement with respect to time, measured in radians per second (rad s⁻¹).

True or False? The time period of a mass-spring system depends on gravitational field strength.

False. The time period of a mass-spring system is independent of the gravitational field strength.

What is a simple pendulum?

A simple pendulum is a system consisting of a string and a bob that swings from side to side.

Define bob in a simple pendulum.

The bob is a mass at the end of the pendulum string, generally spherical and considered a point mass.

True or False? The time period of a simple pendulum depends on gravitational field strength.

True. The time period of a simple pendulum does depend on gravitational field strength.

What is the total energy of a SHM system in terms of kinetic and potential energy?

The total energy of a simple harmonic motion system always remains constant and is equal to the sum of the kinetic and potential energy.

True or False? In SHM, energy is always conserved.

True. In simple harmonic motion, the total energy in the system remains constant and is conserved.

Define kinetic energy in the context of SHM.

Kinetic energy, in the context of SHM, is the energy an object possesses due to its motion.

What happens to the kinetic energy of a mass-spring system at the equilibrium position?

At the equilibrium position, the kinetic energy of a mass-spring system is at its maximum .

How does gravitational potential energy change as a pendulum swings down from its highest point?

As a pendulum swings down from its highest point, gravitational potential energy decreases while kinetic energy increases.

What is the shape of the potential energy graph of an object undergoing half an oscillation from its amplitude position?

The shape of the potential energy graph of an object undergoing half an oscillation from its amplitude position is a U shape.

Which form of energy is at its maximum when a pendulum bob is at its highest point in its swing?

When a pendulum bob is at its highest point in its swing, the gravitational potential energy is at its maximum .

IBPhysicsDPSLFlashcardsWave BehaviourSimple Harmonic Motion

Simple Harmonic Motion (DP IB Physics)

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FrontDescribing Oscillations
How many oscillations are shown by the pendulum in the diagram?

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Cards in this collection (47)

How many oscillations are shown by the pendulum in the diagram?
The pendulum in the diagram shows one oscillation.
What is an oscillation?
An oscillation is the repetitive variation with time of the displacement of an object about the equilibrium position ( $x = 0$ ).
Define the term equilibrium position in simple harmonic motion.
The term equilibrium position in simple harmonic motion is the position where there is no resultant force acting on an object.
What does displacement mean in oscillations?
Displacement in oscillations is the horizontal or vertical distance of a point on the wave from its equilibrium position.
True or False?
The period of an oscillation is measured in seconds.
True.
The period of an oscillation is measured in seconds (s).
What is the amplitude of an oscillation?
The amplitude of an oscillation is the maximum value of the displacement on either side of the equilibrium position.
State the meaning of frequency in terms of oscillations.
Frequency is the number of oscillations per second and it is measured in hertz (Hz).
Define angular frequency.
Angular frequency is the change of angular displacement with respect to time and is measured in radians per second (rad s⁻¹).
State the equation for angular frequency.
The equation for angular frequency is: $ω = \frac{2 π}{T} = 2 π f$
Where:
- $ω$ = angular frequency, measured in radians per second (rad s^-1)
- $T$ = time period, measured in seconds (s)
- $f$ = frequency, measured in hertz (Hz)
How do you calculate the time period, $T$ , of an oscillation?
The time period, $T$ , of an oscillation is calculated using the equation: $T = \frac{1}{f}$
Where:
- $T$ = time period, measured in seconds (s)
- $f$ = frequency, measured in hertz (Hz)
What is simple harmonic motion (SHM)?
Simple harmonic motion (SHM) is a type of oscillation where the restoring force is directly proportional to the displacement and directed towards the equilibrium position.
True or False?
In SHM, the time interval of each complete vibration is the same.
True.
In SHM, the time interval of each complete vibration, known as the period, is constant.
What are the two properties of the restoring force in simple harmonic motion?
The two properties of the restoring force in simple harmonic motion are that:
- it is always directed towards the equilibrium position
- it is proportional to the displacement from the equilibrium position
State one example of an object undergoing SHM.
Examples of objects undergoing SHM are:
- The pendulum of a clock
- A child on a swing
- A rope bridge
- A marble in a bowl
- A bowl set vibrating
- A mass oscillating on a spring
- A bungee jumper coming to a stop at the end of their fall
How does acceleration relate to displacement in SHM?
In SHM, acceleration is proportional to displacement and in the opposite direction to it.
What is the defining equation of SHM?
The defining equation of SHM is: $a = - ω^{2} x$
Where:
- $a$ = acceleration, measured in metres per second squared (m s²)
- $ω$ = angular frequency, measured in radians per second (rad s^-1)
- $x$ = displacement, measured in metres (m)
True or False?
The period of oscillation in SHM depends on the amplitude of oscillation.
False.
The period of oscillation in SHM is independent of the amplitude for small angles of oscillation.
Define angular frequency in the context of SHM.
Angular frequency in SHM is the change of angular displacement with respect to time, measured in radians per second (rad s⁻¹).
State the quantity on the vertical axis of the graph.
The quantity on the vertical axis of the graph is displacement.
State the quantity on the vertical axis of the graph.
The quantity on the vertical axis of the graph is acceleration.
State the direction of the restoring force on the mass shown in the diagram when released from its lowest vertical displacement.
The direction of the restoring force on the mass shown in the diagram when released from its lowest vertical displacement is upwards.
What is the equation for the restoring force in a mass-spring system?
The equation for the restoring force in a mass-spring system is: $F = - k x$
Where:
- $F$ = restoring force, measured in newtons (N)
- $k$ = spring constant, measured in newtons per kilogram (N kg^-1)
- $x$ = spring extension, measured in metres (m)
State the equation for the time period of a mass-spring system oscillating with simple harmonic motion.
The equation for the time period of a mass-spring system oscillating with simple harmonic motion is: $T = 2 π \sqrt{\frac{m}{k}}$
Where:
- $T$ = time period, measured in seconds (s)
- $m$ = mass of spring, measured in kilograms (kg)
- $k$ = spring constant, measured in newtons per kilogram (N kg^-1)
What does $k$ represent in the mass-spring time period equation?
In the mass-spring time period equation, $k$ represents the spring constant, measured in N m⁻¹.
True or False?
The time period of a mass-spring system depends on gravitational field strength.
False.
The time period of a mass-spring system is independent of the gravitational field strength.
How does the spring constant, $k$ , affect the time period of a mass-spring system?
The higher the spring constant, $k$ , the stiffer the spring and the shorter the time period of the oscillation.
What is the restoring force on a mass of 0.2 kg attached to a spring with a spring constant of 90 N m⁻¹ extended by 0.05 m?
The restoring force is: -4.5 N.
- $F = - k x$
- $F = - 90 \times 0.05 = - 4.5 N$
How do you calculate the frequency of a mass-spring system with a mass of 2.0 kg and a spring constant of 0.9 N m⁻¹?
The frequency of the mass-spring system is 0.11 Hz
- $f = \frac{1}{T} = \frac{1}{2 π} \sqrt{\frac{k}{m}}$
- $f = \frac{1}{2 π} \sqrt{\frac{0.9}{2.0}} = 0.11 Hz$
What is a simple pendulum?
A simple pendulum is a system consisting of a string and a bob that swings from side to side.
Define bob in a simple pendulum.
The bob is a mass at the end of the pendulum string, generally spherical and considered a point mass.
What does $L$ represent in the period of a pendulum equation?
In the period of a pendulum equation, $L$ represents the length of the string from the pivot to the centre of mass of the bob.
State the equation for the time period of a simple pendulum.
The equation for the time period of a simple pendulum is: $T = 2 π \sqrt{\frac{L}{g}}$
Where:
- $T$ = time period, measured in seconds (s)
- $L$ = length of string, measured in metres (m)
- $g$ = gravitational field strength, measured in newtons per kilogram (N kg^-1)
True or False?
The time period of a simple pendulum depends on gravitational field strength.
True.
The time period of a simple pendulum does depend on gravitational field strength.
Define small angle approximation.
Small angle approximation is when the angle of oscillation is less than 10°, allowing $\sin θ$ to be approximated as $θ$ .
What is the restoring force in a simple pendulum?
The restoring force in a simple pendulum is the component of the weight force acting along the arc of the circle towards the equilibrium position. It is given by the equation: $F = - m g \sin θ$
State the equation that relates angular frequency and time period.
The equation for angular frequency and time period is $ω = \frac{2 π}{T}$
Where:
- $ω$ = angular frequency, measured in radians per second (rad s^–1)
- $T$ = time period, measured in seconds (s)
What is the angular frequency of a pendulum with a length of 0.8 m on Earth with a gravitational field strength of 9.81 m s^–²?
The angular frequency is 3.5 rad s^-1
- $ω = \sqrt{\frac{g}{l}}$
- $ω = \sqrt{\frac{9.81}{0.8}} = 3.5 rad s^{- 1}$
What is the total energy of a SHM system in terms of kinetic and potential energy?
The total energy of a simple harmonic motion system always remains constant and is equal to the sum of the kinetic and potential energy.
What is the equation for elastic potential energy?
The equation for elastic potential energy is: $E_{p} = \frac{1}{2} k x ²$
Where:
- $E_{p}$ = elastic potential energy, measured in joules (J)
- $k$ = spring constant, measured in newtons per metre (N m^-1)
- $x$ = extension, measured in metres (m)
True or False?
In SHM, energy is always conserved.
True.
In simple harmonic motion, the total energy in the system remains constant and is conserved.
Define kinetic energy in the context of SHM.
Kinetic energy, in the context of SHM, is the energy an object possesses due to its motion.
State the relationship between kinetic energy and potential energy in SHM.
The relationship between kinetic energy and potential energy in SHM is: $E = E_{p} + E_{k}$
Where:
- $E$ = the total energy, measured in joules (J)
- $E_{p}$ = potential energy, measured in joules (J)
- $E_{k}$ = kinetic energy, measured in joules (J)
What happens to the kinetic energy of a mass-spring system at the equilibrium position?
At the equilibrium position, the kinetic energy of a mass-spring system is at its maximum.
How does gravitational potential energy change as a pendulum swings down from its highest point?
As a pendulum swings down from its highest point, gravitational potential energy decreases while kinetic energy increases.
What is the shape of the potential energy graph of an object undergoing half an oscillation from its amplitude position?
The shape of the potential energy graph of an object undergoing half an oscillation from its amplitude position is a U shape.
Which form of energy is at its maximum when a pendulum bob is at its highest point in its swing?
When a pendulum bob is at its highest point in its swing, the gravitational potential energy is at its maximum.
Identify the quantity represented by the horizontal line in the graph.
The quantity represented by the horizontal line on the graph is total energy.