Chapter 19 Oscillations

Which of the following statements about an object which performs simple harmonic motion is true?

• The acceleration is zero when the displacement is maximum.

• The velocity is maximum when the displacement is zero.

• The velocity is directly proportional to the displacement.

• The acceleration is positive when the displacement is positive.

A particles is in simple harmonic motion. When its displacement from a point O is x, the acceleration of the particle is -kx. The period T of the simple harmonic motion is

• $2\pi k$

• $2\pi\sqrt{k}$

• $\frac{2\pi}{k}$

• $\frac{2\pi}{\sqrt{k}}$

The variation with time t of the displacement x of a particle in simple harmonic motion form point O is given as x=5.0 sin 20t. What is the period of the simple harmonic motion?

• 0.050 s

• 0.20 s

• 0.22 s

• 0.31 s

A particle is in simple harmonic motion. The amplitude of the motion is 3.0 m and the frequency is 20 Hz. At time t=0, the displacement of the particle from the equillibrium position is x=+3.0 m. Which equation correctly represents the variation of displacement x with time t?

• x=3.0 sin $20\pi t$

• x=3.0 sin $40\pi t$

• x=3.0 cos $20\pi t$

• x=3.0 cos $40\pi t$

At the instant t₁, the displacement is 2.5 cm. What is the displacement 1.0 s after t₁?

• 0 cm

• -2.5 cm

• 2.5 cm

• 5.0 cm

The displacement of a particle moving in simple harmonic motion is given by x=5 cos 2t where x is in centimetres and the time t in seconds. If the period of the motion is T, the acceleration of the particle at t= $\frac{T}{6}$  is

• -17.3 cm  $s^{-2}$  

• -10.0 cm  $s^{-2}$  

• +10.0 cm  $s^{-2}$  

• +17.3 cm  $s^{-2}$  

The graph shows the variation of displacement x against time t of a body in simple harmonic motion. Which statement is true?

• The period is 0.30 s.

• The angular frequency is 0.40 s^-1.

• The frequency is 2.5 Hz.

• The amplitude is 10.0 cm.

An object moves with simple harmonic motion with amplitude A. What is the position x of the object when the kinetic energy of the object equals twice its potential energy?

• $\frac{1}{\sqrt{3}}A$

• $\frac{1}{\sqrt{2}}A$

• $\frac{1}{3}A$

• $\frac{1}{2}A$

A body of mass m performs simple harmonic motion with angular frequency  $\omega$ . The maximum kinetic energy of the body is K. What is the amplitude of oscillation?

•  $\sqrt{\frac{K}{2m\omega^2}}$  

•  $\sqrt{\frac{2K}{m\omega^2}}$  

•  $\sqrt{\frac{2K\omega^2}{m}}$  

•  $\sqrt{\frac{K\omega^2}{2m}}$  

A particle is in simple harmonic motion of amplitude 5.0 cm and period of 2.4 s. At time t=0, it is at x= -5.0 cm. Write the equation to represent the variation of displacement x with time t. Please write $\pi$ as pi

(a)