10 minutes maximum! Can you do it in 5?

Q1+2: A tall radio mast is swaying in a strong wind. The time period is 2 s and the amplitude of the motion of the top of the mast is 0.5 m. The motion can be assumed to be SHM.

  

 1. What is the value of ω?

  • A. ½π rad s-1
  • B. π rad s-1
  • C. 2π rad s-1
  • D. 4π rad s-1

2. What is the value of the acceleration when x = 0.5 m?

  • A. ½π2 ms-2
  • B. π2 ms-2
  • C. 2π2 ms-2
  • D. 14π2 ms-2

The following 4 graphs are to used for questions 3- 5:

Which of these graphs shows the variation with displacement of..

  
3. ...the kinetic energy of an SHM system?
4. ...the potential energy of an SHM system?
5. ...the total kinetic energy and potential energy of an SHM system?

 

Q6-8.

A 2 kg mass on a spring is oscillating as shown. This is a simple harmonic oscillation, with a time period of 1 second and an amplitude of 10 cm.

 

 
oscillating mass on a spring

6. What is the total energy of this oscillating system in joules?

  • A. 2 π2
  • B. 0.4 π2
  • C. 0.02 π2
  • D. 0.04 π2

7. What is the maximum velocity v of the mass in ms-1?

  • A. 0.1 π
  • B. 0.2 π
  • C. 0.4 π
  • D. π

8. The graph shown here gives the displacement of the mass from the centre point at a time T.

SHM displacement time graph

Which of the following graphs shows the variation of velocity at a time T?
SHM velocity time graph options x4

 

9+10. A pendulum is pulled to the left and then released. It then performs simple harmonic motion as shown here, with a frequency of 0.5 Hz and amplitude x0.

 

pendulum gif wikimedia

Stündle | CC BY-SA 4.0

9. In the formula x = x0 sin (ωt + φ), what is the value of the phase angle φ for the pendulum at this starting position?

  • A. 0
  • B. ¼ π
  • C. ½ π
  • D. π

10. What is the speed of the pendulum when the displacement is ½ x0?

  • A. ${\sqrt{3} \over 2} \pi$
  • B. ${\sqrt{3} \over 4} \pi$
  • C. ${3 \over 4} \pi$
  • D. ${1 \over 4} \pi$