First slide

Simple harmonic motion

Question

A simple harmonic wave having an amplitude a and time period T is represented by the equation $y = 5 sinπ (t + 4) m .$ Then the value of amplitude (a) in (m) and time period (T) in second are

Moderate

A

$a = 10, T = 2$
B

$a = 5, T = 1$
C

$a = 10, T = 1$
D

$a = 5, T = 2$

Solution

$y = 5 \sin (π t + 4 π)$ , comparing it with standard equation
$y = asin (ω t + φ) = asin (\frac{2 π t}{T} + φ)$
$a = 5 m$ and $\frac{2 π t}{T} = π t \Rightarrow$ T = 2 sec.

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