Question

If the differential equation for a simple harmonic motion is \( \frac{d^2 y}{dt^2} + 2y = 0 \), the time-period of the motion is:

• A. \( \pi \sqrt{2} \) sec
• B. \( \sqrt{5} \sec \)
• C. \( \frac{\pi}{\sqrt{2}} \) sec
• D. \( 2\pi \sec \)

Hint:

For simple harmonic motion, the time period is determined by the angular frequency \( \omega \), where \( T = \frac{2\pi}{\omega} \).

Answer 1

The Correct Option is C

For simple harmonic motion, the equation is of the form: \[ \frac{d^2 y}{dt^2} + \omega^2 y = 0 \] Comparing with the given equation \( \frac{d^2 y}{dt^2} + 2y = 0 \), we find \( \omega^2 = 2 \). The time period \( T \) is given by: \[ T = \frac{2\pi}{\omega} = \frac{\pi}{\sqrt{2}} \]
Final Answer: \[ \boxed{\frac{\pi}{\sqrt{2}} \, \text{sec}} \]