IB Physics HL C 1 9 Hl Shm Equations Questions

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.

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Study C.1.9 (HL)—SHM equations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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

Figure for Question IB Physics HL C 1 9 Hl Shm Equations Questions 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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IB Physics HL C 1 9 Hl Shm Equations Questions question 1