First slide

Simple harmonic motion

Question

Two simple harmonic motions are represented by equations
$\begin{array}{l} y_{1} = 4 \sin (10 t + ϕ) \\ y_{2} = 5 \cos 10 t \end{array}$
What is the phase difference between their velocities?

Moderate

A

$ϕ$
B

$- ϕ$
C

$(ϕ + \frac{π}{2})$
D

$(ϕ - \frac{π}{2})$

Solution

$\begin{array}{l} y_{1} = 4 \sin (10 t + ϕ), y_{2} = 5 \cos 10 t \\ v_{1} = \frac{d y_{1}}{d t} = 40 \cos (10 t + ϕ) \\ v_{2} = \frac{d y_{2}}{d t} = - 50 \sin 10 t = 50 \cos (10 t + \frac{π}{2}) \end{array}$
$Phase difference between v_{1} and v_{2} = (ϕ - \frac{π}{2})$

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