Instantaneous Displacement in SHM – Rankers Physics
Topic: Oscillation
Subtopic: Equation of SHM

Instantaneous Displacement in SHM

A body oscillates in SHM according to the equation \( x = 10 cos \left(2\pi t + \frac{\pi}{4} \right)\text{ cm}\). Its instantaneous displacement at \(t = 1\text{ s}\) is
10 cm
\(\frac{5}{\sqrt{2}}\text{ cm}\)
\[5\sqrt{2}\text{ cm}\]
\[10\sqrt{2}\text{ cm}\]

Solution:

Substituting \(t = 1\text{ s}\) in the given equation: \[x = 10 cos\left(2\pi(1) + \frac{\pi}{4}\right) = 10 cos\left(\frac{\pi}{4}
/right) = \frac{10}{\sqrt{2}} = 5\sqrt{2}\text{ cm}\].

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