Cambridge International A Level · Physics (9702)
5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Oscillations.
A simple pendulum undergoes undamped simple harmonic motion. Which of the following statements correctly describes the relationship between the acceleration \( a \) of the pendulum bob and its displacement \( x \) from the equilibrium position?
An object of mass \( m \) undergoes simple harmonic motion with an amplitude \( x_0 \).
At which displacement \( x \) from the equilibrium position is the kinetic energy of the object equal to three times its potential energy?
Two particles, X and Y, are oscillating in simple harmonic motion about the same equilibrium position along the same straight line. Both particles have an amplitude of oscillation equal to A and the same frequency. There is a constant phase difference of \(\frac{\pi}{3}\) rad between their motions.
What is the maximum distance between the two particles during the oscillation?
A particle is undergoing simple harmonic motion about a fixed equilibrium position. Which statement correctly describes the relationship between its acceleration \( a \) and its displacement \( x \) from the equilibrium position?
A particle of mass \( 0.50\text{ kg} \) is undergoing simple harmonic motion. The variation with the square of its displacement \( x^2 \) of the square of its velocity \( v^2 \) is shown in the graph as a straight line. The intercept on the \( v^2 \)-axis is \( 0.16\text{ m}^2\text{s}^{-2} \) and the intercept on the \( x^2 \)-axis is \( 4.0 \times 10^{-4}\text{ m}^2 \).
What is the total energy of the oscillating particle?
A simple pendulum has a period of \( 2.0\text{ s} \). Calculate its angular frequency \( \omega \) in \( \text{rad s}^{-1} \).
Write your answer out first, then check it against the worked solution.
Explain how the amplitude of a forced oscillation at the resonance frequency changes when the degree of damping in the system is increased.
Write your answer out first, then check it against the worked solution.
A particle in simple harmonic motion has displacement \( x = x_0 \sin(\omega t) \). Determine the displacement, in terms of the amplitude \( x_0 \), at which the kinetic energy of the particle is exactly three times its potential energy.
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(a) Define simple harmonic motion. [2]
(b) A small sphere of mass \( 0.40\text{ kg} \) is undergoing simple harmonic motion with a period of \( 0.80\text{ s} \) and an amplitude of \( 3.0\text{ cm} \). Calculate the maximum speed of the sphere. [2]
Write your answer out first, then check it against the worked solution.
An object is oscillating with simple harmonic motion of amplitude \( x_0 \).
(a) Describe the interchange between kinetic energy and potential energy during one complete oscillation, starting from the equilibrium position. [2]
(b) Show that the displacement \( x \) at which the kinetic energy of the object is equal to three times its potential energy is given by \( x = \pm 0.50x_0 \). [3]
Write your answer out first, then check it against the worked solution.
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