Question

A spring has natural length $40cm$ and spring constant $500N/m$.A block of mass $1kg$ is attached at one end of the spring and other end of the spring is attached to ceiling. The block released from the position, where the spring has length $45cm$, then

• A. the block will perform SHM of amplitude $5cm$
• B. the block will have maximum velocity $30\sqrt{5}cm/sec$
• C. the block will have maximum acceleration $15m/s^2$
• D. the minimum potential energy of the spring will be zero

Answer 1

Answer: (B), (C), (D)

The correct options are
B the block will have maximum acceleration $15m/s^2$
C the minimum potential energy of the spring will be zero
D the block will have maximum velocity $30\sqrt{5}cm/sec$

From the image it is clear that, the amplitude of SHM will be $a=3cm$, also
from the given data, $\omega =\sqrt{\frac{k}{m}}=10\sqrt{5}$, thus maximum velocity $v_{max}=a\omega =30\sqrt{5}cm-se{c}^{-1}$
$Acceleratio{n}_{max}=a{\omega }^2=15m-se{c}^{-2}$
Minimum potential energy is $0$ at mean position.