First slide

Simple harmonic motion

Question

A particle is executing a motion in which its displacement as a function of time is given by $x = 3 \sin (5 π t + π / 3) + \cos (5 π t + π / 3)$ where x is in m and t is in s. Then the motion is

Moderate

A

simple harmonic with time period 0.2 s
B

simple harmonic with time period 0.4 s
C

simple harmonic with amplitude 3 m
D

not a simple harmonic but a periodic motion

Solution

$\begin{array}{l} x = 3 \sin (5 π t + π / 3) + \cos (5 π t + π / 3) \\ Amplitude = x_{max} = \sqrt{3^{2} + 1^{2}} = \sqrt{10}, ω = 5 π \\ T = \frac{2 π}{ω} = \frac{2 π}{5 π} = 0.4 s \end{array}$

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