# IB DP Physics 9.1 – Simple harmonic motion Question Bank SL Paper 1

### Question

A particle executes simple harmonic motion (SHM) with period T.

Which sketch graph correctly shows how the total energy E of the particle varies with time t from t = 0 to $$t = \frac{T}{2}$$?

## Markscheme

D

Total Energy is constant.

### Question

A particle of mass $$m$$ oscillates with simple harmonic motion (SHM) of angular frequency $$\omega$$. The amplitude of the SHM is $$A$$. What is the kinetic energy of the particle when it is half way between the equilibrium position and one extreme of the motion?

A.     $$\frac{{m{A^2}{\omega ^2}}}{4}$$

B.     $$\frac{{3m{A^2}{\omega ^2}}}{8}$$

C.     $$\frac{{9m{A^2}{\omega ^2}}}{{32}}$$

D.     $$\frac{{15m{A^2}{\omega ^2}}}{{32}}$$

= $$K(t)=\frac{1}{2}mv^2 =\frac{1}{2}mw^2x_m^2sin^2(wt+\phi )$$
Given in the question  $$y=\frac{A}{2}$$
$$\therefore K.E = \frac{1}{2}mw^2(A^2-(\frac{A}{2})^2 )$$
$$=\frac{3}{8}mw^2A^2$$