IB Physics HL C 1 9 Hl Shm Equations Questions

Use initial position and direction to choose the phase of an HL simple harmonic motion model, then calculate instantaneous velocity and maximum speed.

Exam points

Calculate maximum SHM speed from amplitude and angular frequency, using frequency or period to find angular frequency.
Choose the velocity equation and its sign from an initial displacement at the negative extreme.
Calculate velocity at a specified time from a sinusoidal displacement model with a non-zero initial phase.

[Maximum number: 2]

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