Question

A block is kept on a frictionless horizontal table and connected to a spring attached to a wall. Spring constant 'k' is known but the mass of the block 'm' is unknown. X and Y are the extreme positions of the motion and at O, the spring is in its natural length. Spring constant is 'k'.

Distance between O and Y is $d$. If $\omega =\sqrt{\frac{k}{m}}$, what is the speed at point O?

• A. $\frac{d\omega }{2}$
• B. $d\omega$
• C. $2d\omega$
• D. $d^2\omega$
• E. $d{\omega }^2$

Answer 1

Answer: (B)

$d\omega$

When the block at Y , the potential energy of the spring is $U=\frac{1}{2}k{d}^2$

When the block passes through the equilibrium position, O , this potential energy is completely converted to kinetic energy.

So, $\frac{1}{2}k{d}^2=\frac{1}{2}m{v}^2$

or $v=d\sqrt{k/m}=dw$