SHM (CIE A-level)

The acceleration a of a simple harmonic oscillator is related to its displacement x by the equation a = − 25 x.

What is the frequency of the oscillator?

• 0.80 Hz

• 1.3 Hz

• 4.0 Hz

• 5.0 Hz

A pendulum is oscillating in air and experiences damping.

Which of the following statements is/are correct for the damping force acting on the pendulum?

1 It is always opposite in direction to acceleration.

2 It is always opposite in direction to velocity.

3 It is maximum when the displacement is zero.

• Only 1 and 2

• Only 2 and 3

• Only 3

• 1, 2 and 3

An object oscillates with simple harmonic motion.

Which graph best shows the variation of its potential energy E with distance x from the equilibrium position?

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A tensile force of 4.5 N is applied to a spring. The spring extends elastically by 3.2 cm.

What is the elastic potential energy of the spring?

• 0.072 J

• 0.14 J

• 2.4 J

• 14 J

• 7.1 x 10^-3 J

• 0.188 J

• 0.99 J

• 1.26 J

State the meaning of natural frequency.

• Radial or circular frequency, measures angular displacement per unit time.

• Occur when an oscillating system is driven by a periodic force that is external to the oscillating system.

• An oscillation that fades away with time.

• Frequency at which object vibrates when free to do so.

A particle of mass m performs SHM with an amplitude a and frequency f.

The total energy of this SHM is

• $\frac{1}{2}ma^2f^2$
  

• $2ma^2f^2$
  

• $2\pi^2ma^2f^2$

  
  

• $4\pi^2ma^2f^2$

Which of the following statements is true for a damped system of oscillation?

• The system does not oscillate at its natural frequency.

• When resonance takes place, the system does not lose energy.

• Damping causes the oscillating frequency to become gradually smaller.

• The oscillating amplitude is maximum when forced frequency is almost the same as the natural frequency.