Solveeit Logo
Login

Question

Question: The equation of motion of a particle is \(\frac{d^{2}y}{dt^{2}} + Ky = 0\), where K is positive cons...

The equation of motion of a particle is d2ydt2+Ky=0\frac{d^{2}y}{dt^{2}} + Ky = 0, where K is positive constant. The time period of the motion is given by

A

2πK\frac{2\pi}{K}

B

2πK2\pi K

C

2πK\frac{2\pi}{\sqrt{K}}

D

2πK2\pi\sqrt{K}

Answer

2πK\frac{2\pi}{\sqrt{K}}

Explanation

Solution

On comparing with standard equation d2ydt2+ω2y=0\frac{d^{2}y}{dt^{2}} + \omega^{2}y = 0 we get ω2=K⇒ω=2πT=K⇒T=2πK\omega^{2} = K \Rightarrow \omega = \frac{2\pi}{T} = \sqrt{K} \Rightarrow T = \frac{2\pi}{\sqrt{K}}.