IB Physics HL C.1.9 Simple Harmonic Motion Equations Question Bank

Practise IB Physics HL C.1.9 by choosing sine or cosine from initial conditions and calculating displacement, velocity and maximum speed.

Exam points

Choose x = A sin(ωt + φ) or cosine form from the initial position and direction.
Differentiate the displacement equation to calculate velocity and acceleration with phase.
Use v_max = ωA and phase-shifted equations to calculate speed at a stated time.

[Maximum number: 2]

A boat is moved from land to water by rolling it across a set of cylindrical airbags.

Figure for Question C.1.9 (HL)—SHM equations question 1 — IB Physics HL

During the testing of the rod, it is rotated about its central axis. Point P is on the surface of the rod. At time t=0, P is at a point $45^{\circ}$ above the horizontal. The linear speed of P is $2.0 \mathrm{~ms}^{-1}$ .

The vertical displacement x of P can be modelled with an equation $x=x_{0} \sin (\omega t+\phi)$ .

Determine the vertical velocity of P at $t=3.0 \mathrm{~s}$ .

Use of $v=\omega x_{0} \cos (\omega t+\phi)$ and $\phi=\frac{\pi}{4}$ $v=\omega x_{0} \cos (\omega t+\phi)=(2.22)(0.9) \cos \left((2.22)(3)+\frac{\pi}{4}\right)=0.79 m s^{-1} \quad$

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C.1.9 (HL)—SHM equations question 1