10 minutes maximum! Can you do it in 5?

 1. Simple Harmonic Motion (SHM) is defined as an oscillation where ..

  • A. acceleration is proportional to the displacement from the centre.
  • B. acceleration is proportional to the speed of the oscillation.
  • C. acceleration is proportional to the velocity of the oscillation.
  • D. acceleration is proportional to the mass of the system.

2. The acceleration of the system is always..

  • A. directed to the left.
  • B. directed to the right.
  • C. in the opposite direction to the displacement from the centre.
  • D. in the same direction to the displacement from the centre.

3. A spring oscillates up and down with a frequency of 4 Hz. The angular velocity ω is:

  • A. 2π
  • B. 8π
  • C. ${2 \over \pi}$
  • D. ${8 \over \pi}$

 

4 - 7. The graph below shows how the displacement of a pendulum mass varies with time.

sine wave graph no y axis label

pendulum gif wikimedia

Stündle | CC BY-SA 4.0

4. Which of the graphs below shows how the acceleration of the mass varies with the displacement, x?

graph to show acceleration against dispacement for SHM x4

5. The pendulum has a time period of π seconds. The length of the pendulum is approximately:

  • A. 0.25 m
  • B. 1.6 m
  • C. 2.5 m
  • D. 5 m

6. Which of the following best describes the velocity and the acceleration of the mass at the centre of the oscillation?

 velocity Acceleration
A
 zero zero
B
 zero maximum
C
 maximum zero
D
 maximum maximum

7. Which of the following best describes the potential and kinetic energy of the mass at the maximum displacement?

 Potential Energy Kinetic Energy
A
 zero zero
B
 zero maximum
C
 maximum zero
D
 maximum maximum

8. SHM is present in many oscillating systems. Which of the following is NOT an 'SHM oscillation'?

  • A. A mass bouncing up and down on a spring
  • B. A column of water oscillating in a U shaped tube.
  • C. The end of a ruler vibrating backwards and forwards.
  • D. A ball bouncing up and down on the floor.

 

9+10: A mass m oscillates up and down on a spring of spring constant k.

The time period of the oscillation is 1 second.

At a displacement of x from the equilibrium position, the acceleration is a.

 

 

 oscillating mass on a spring

9. What is the absolute value of ${a \over x}$?

  • A. π
  • B. 2π
  • C. 2π2
  • D. 4π2

10. The spring is replaced with one with a spring constant of 16k and a mass of 4m is added. The new time period is:

  • A. 0.25 s
  • B. 0.5 s
  • C. 2 s
  • D. 4 s