First slide

Simple hormonic motion

Question

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

Moderate

A

$\emptyset$
B

- $\emptyset$
C

$(\emptyset + \frac{π}{2})$
D

$(\emptyset - \frac{π}{2})$

Solution

$y_{1} = 4 \sin (10 t + \emptyset)$
$y_{2} = 5 \cos 10 t$
$v_{1} = \frac{{dy}_{1}}{dt} = 40 \cos (10 t + \emptyset)$
$v_{2} = \frac{{dy}_{2}}{dt} = - 50 \sin 10 t = 50 \cos (10 t + \frac{π}{2})$
Phase difference between $v_{1} and v_{2} = (\emptyset - \frac{π}{2})$

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