Simple Harmonic Motion (HL IB Physics)

A point on a guitar string S oscillates about its equilibrium position Z in simple harmonic motion.

The amplitude of the oscillation is YZ.

Which positions show when the acceleration of point S is at a maximum and the velocity of point S is at zero?

A simple pendulum and a mass-spring system oscillate about their equilibrium positions with simple harmonic motion. On Earth, the period of the oscillations is T. The pendulum and the mass-spring system are taken to Mars where the acceleration of free fall is smaller than on Earth.

Which answer best describes the period of the pendulum and the mass-spring system on Mars?

Identify the quantities that remain constant to meet the criteria for an object oscillating in simple harmonic motion. 

A mass-spring system oscillates with simple harmonic motion. The mass m has an amplitude A and the spring has a total energy E. The mass is increased by half and the amplitude increased to 4A.

What is the total energy in the spring E_T?

A pendulum oscillating with simple harmonic motion has an amplitude and a maximum kinetic energy E_k.

What is the potential energy of the system when the pendulum bob is at a distance 0.4 from its maximum displacement?

Which of the following is a correct arrangement for the maximum displacement of a particle performing simple harmonic motion?

An ion in a crystal lattice structure oscillates with simple harmonic motion. The period of the oscillation is T. T is measured from equilibrium.

Which graph shows the change in kinetic energy of the ion from time t = 0 to t = ?

A simple pendulum performs simple harmonic motion. The pendulum bob has a mass m, the string has a length l, and the pendulum has a period T. 

Which is the correct value for the period T₁ if the mass of the pendulum bob is doubled and the length of the string is halved?

A mass-spring system oscillates about its equilibrium position in simple harmonic motion. A bulb on the motion sensor lights up each time the block passes the equilibrium position.

The block has a mass m and oscillates with a period T. 

Select the new mass that would cause the period to double.

A simple pendulum oscillates with simple harmonic motion as shown.

At which positions are the acceleration at zero, the displacement at a negative maximum, and velocity at a maximum?

A mass-spring system is oscillating with simple harmonic motion.

What is the total energy of the object proportional to?

Which line identifies quantities which always have opposite directions during simple harmonic motion?

The graph shows the variation with time t of the acceleration a of an object X undergoing simple harmonic motion (SHM).

A second object Y oscillates with the same frequency as X but with a phase difference of  .

Which graph shows how the acceleration of object Y varies with t?

A particle, P, oscillates on the line XZ about its equilibrium point Y, in simple harmonic motion.

At the point shown, which statement could be correct about the motion of the particle?

A pendulum is undergoing simple harmonic motion with a time period T and angular frequency ω.

A student makes a change to the set up so that the pendulum has a new time period 3T.

What is the new angular frequency?

A pendulum is made to swing by a student pulling the bob to the left and releasing it. The student is careful to displace the bob by only a small amount.

After two full oscillations, the motion of the pendulum is plotted on a graph.

At which point is the velocity of the bob towards the right?

A mass is attached to a vertical spring and allowed to reach equilibrium. It is then displaced by a distance d and released. The total energy and time period are E_T and T respectively.

In a second investigation the same mass-spring system travels twice as fast.

Which line correctly identifies the total energy and time period of the second oscillations?

	ET	T
A.	2E
B.	4E
C.	2E	2T
D.	4E	T

Which of the following graphs shows the variation with displacement x of the speed v of a particle performing simple harmonic motion?

Which graph correctly represents the relationship between acceleration, a, and displacement, x, in simple harmonic motion?

The graph shows the motion of an oscillating body.

What is the frequency of the oscillation?

The following graph shows the acceleration as a function of time for a simple pendulum oscillating isochronously. 

Which of the following gives the times at which kinetic energy is at a maximum?

A mass-spring system is set up horizontally on a frictionless surface. The spring is extended to the left and released so that the mass oscillates in SHM.

Taking motion to the left to be positive, which of the following statements is correct about the motion of the mass?

An object oscillates about its equilibrium position periodically. It has a total energy E and period T. The amplitude is reduced to one quarter of the original amplitude.

What is the new total energy and period of the system?

	Total energy	Period
A.
B.
C.
D.

A simple pendulum and a mass-spring system are set up such that the periods of the oscillations are equal. The mass of the pendulum and the mass-spring system are initially identical. The set-up is repeated, but this time the masses of both systems are reduced to three quarters of their original mass.

What is the ratio of the time period of the pendulum to the time period of the mass-spring system after the masses have been changed?

A simple pendulum oscillates with a time period T near the surface of the Earth. The same pendulum is moved to the surface of the Moon, where the acceleration of free fall is 0.2 g.

What is the value of T for the pendulum near the surface of the moon?

A body of mass 0.40 kg is subjected to a force F which varies with its displacement x from a fixed point as shown in the graph below.

What is the maximum velocity of the body?

A satellite rotates clockwise around a planet of radius r with an angular velocity ω. The satellite passes position S at time zero and position P at time t. Q is the projection of P onto the diameter through S. Measured with respect to the origin O, the displacement, linear velocity and linear acceleration of Q in the direction OS are x, v, and a respectively. 

Which option gives the correct equations for x, v and a?

A.
B.
C.
D.

A small ball bearing oscillates in simple harmonic motion. 

Which is a correct expression for the kinetic energy per unit mass of the ball bearing?

The table below shows the values for the acceleration and displacement of a particle moving isochronously.

What is the period of the motion?

A pendulum bob is suspended by a thread. The bob is moved to the right and released so that the pendulum oscillates isochronously. 

Taking motion to the left to be positive, which of the following statements is incorrect about the motion of the pendulum?

When an object oscillates in simple harmonic motion, a restoring force acts toward the equilibrium position.

Which graph shows the restoring force, F, as a function of displacement, x?

The graph below shows the displacement as a function of time for a particle in SHM.

At certain points in the oscillation, the acceleration and velocity act in opposite directions. 

Which letter indicates such a point?

A mass is attached to a spring from above and the spring is secured to a clamp. The mass is pulled down and released resulting in a simple harmonic oscillation. 

Which one of the following statements is true?

A pendulum bob on a string oscillates in SHM with a frequency, f. 

The period, T, of a simple pendulum is related to the length of the string, l, and the acceleration of free fall, g, by the following equation:

What would the ratio be of the original frequency to the new frequency if the length of the string was increased by a factor of 4?

A simple pendulum oscillates in SHM.

Which row correctly describes the force, F, acceleration, a, and velocity, v, at position Y?

The total energy, E_T, of a mass-spring system in SHM is related to the mass, m, angular speed, ω, and the amplitude, A, by the following equation:

What is the ratio of the original amplitude to the new amplitude if the mass is reduced by a factor of 4 and the angular speed is halved but the total energy remains the same?

A mass spring system is set up so that the mass glides on a frictionless surface between two springs on a horizontal bench. The mass-spring system performs SHM

Which of the following statements is true?

A mass-spring system has a period, T, mass, m, and a spring constant, k. These quantities are related by the following equation:

A new spring has a spring constant of 3 times the original value.

Using this new spring, which mass would cause the period, T, to decrease by a factor of 6?

The graph below shows the kinetic energy of a simple pendulum as a function of time. The time period of the pendulum is T. 

What does the length of the line JK represent?