Retrieval Practice — Simple Harmonic Motion — Simple Harmonic Motion

Q1. State the two conditions required for simple harmonic motion.

(1) The acceleration is proportional to the displacement. (2) The acceleration is always directed towards the equilibrium position (opposite to displacement).

Q2. Write the defining equation of SHM.

a = -omega^2 x, where a is acceleration, omega is angular frequency, and x is displacement from equilibrium.

Q3. Write the SHM displacement equation and state when to use cosine vs sine.

x = A cos(omega t) when starting from maximum displacement. x = A sin(omega t) when starting from the equilibrium position.

Q4. State the equation for the speed of an oscillator at displacement x.

v = +/- omega sqrt(\(A^{2}\) - \(x^{2}\)).

Q5. State the maximum speed and maximum acceleration of an SHM oscillator.

v_max = omega A (at x = 0). a_max = omega^2 A (at x = +/- A).

Q6. What is the phase relationship between displacement, velocity, and acceleration in SHM?

Velocity leads displacement by 90 degrees (pi/2).
Acceleration leads displacement by 180 degrees (pi).
Acceleration is the reflection of displacement in the time axis.

Q7. State the equation for the time period of a mass-spring system.

T = 2 pi sqrt(m/k), where m = mass and k = spring constant.

Q8. Does the period of a mass-spring system depend on gravity?

No.
T = 2 pi sqrt(m/k) has no g term.
The period is the same on Earth and the Moon.

Q9. State the equation for the time period of a simple pendulum.

T = 2 pi sqrt(L/g), where L = length from pivot to centre of bob, g = gravitational field strength.

Q10. What limitation applies to the simple pendulum equation?

It is only valid for small angles of oscillation (theta < 10 degrees) where the small angle approximation sin theta = theta holds.

Q11. Describe the energy interchange in SHM.

At equilibrium: all kinetic energy, zero potential.
At amplitude: all potential energy, zero kinetic.
Total energy stays constant throughout.

Q12. In the mass-spring required practical, what do you plot and how do you find k?

Plot \(T^{2}\) (y-axis) against mass m (x-axis).
Gradient = 4 pi^2 / k.
So k = 4 pi^2 / gradient.

Q13. In the simple pendulum required practical, what do you plot and how do you find g?

Plot \(T^{2}\) (y-axis) against length L (x-axis).
Gradient = 4 pi^2 / g.
So g = 4 pi^2 / gradient.

Q14. Why do you time 10 oscillations rather than 1?

To reduce the effect of reaction time error.
Dividing 10 oscillations by 10 gives a more accurate mean period.

Q15. Give an example of an oscillation that is not SHM and explain why.

A person bouncing on a trampoline.
When not in contact with the trampoline, the only force is weight, which is constant regardless of displacement.
The restoring force is not proportional to displacement.