Describe the conditions required for an object to perform simple harmonic motion (SHM).

A second identical spring is placed in parallel and the experiment in (b) is repeated. Suggest how this change affects the fractional uncertainty in the mass of the block.

A particle is oscillating with simple harmonic motion (shm) of amplitude x₀ and maximum kinetic energy E_k. What is the potential energy of the system when the particle is a distance 0.20x₀ from its maximum displacement? 

A. 0.20E_k 

B. 0.36E_k 

C. 0.64E_k 

D. 0.80E_k

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

determine the initial energy.

Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

An object undergoing simple harmonic motion (SHM) has a period T and total energy E. The amplitude of oscillations is halved. What are the new period and total energy of the system?

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time t of the velocity v of the ball during one period.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

A mass oscillates with simple harmonic motion (SHM) of amplitude x_o. Its total energy is 16 J. 

What is the kinetic energy of the mass when its displacement is $\frac{x_0}{2}$?

A. 4 J

B. 8 J

C. 12 J

D. 16 J

Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.

Calculate the time taken for the block to return to the equilibrium position for the first time. 

Deduce $\frac{k_1}{k_2}$.

Determine the amplitude of oscillation for test 1.

Estimate the value of k in the following expression.

T = $2\pi \sqrt{\frac{m}{k}}$

Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.

Outline, without calculation, the change to the time period of the system for the model represented by graph B when $a$ is large.

Show that the period of oscillation of the ball is about 6 s.

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

Estimate the displacement needed to double the energy of the string.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Calculate, in terms of g, the maximum acceleration of P.

Calculate the mass of the wooden block.

In carrying out the experiment the student displaced the block horizontally by 4.8 cm from the equilibrium position. Determine the total energy in the oscillation of the wooden block.

The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s^–1.

Calculate the speed of the block as it passes the equilibrium position. 

A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.

Show that the maximum speed of the oscillating plate is about 20 m s⁻¹.

Calculate the period of oscillations of q.

Outline two reasons why both models predict that the motion is simple harmonic when $a$ is small.

The graph shows for model A the variation with $x$ of elastic potential energy E_p stored in the spring.

Describe the graph for model B.

Determine the time period of the system when $a$ is small.

Deduce whether the motion of Z is simple harmonic.