Question

A 10 kg metal block is attached to a spring of spring constant $1000N{m}^{-1}$. A block is displaced from equilibrium position by 10 cm and released. The maximum acceleration of the block is

• A. $10m{s}^{-2}$
• B. $100m{s}^{-2}$
• C. $200m{s}^{-2}$
• D. $0.1m{s}^{-2}$

Answer 1

The correct option is A $10m{s}^{-2}$

Given : $m=10$ kg $k=1000$ $N/m$

Amplitude of oscillation $A=10$ cm $=0.1$ m

Angular frequency of oscillation $w=\sqrt{\frac{k}{m}}=\sqrt{\frac{1000}{10}}=10$ $rad/s$

Maximum acceleration $a_{max}=A{w}^2$

$\therefore$ $a_{max}=0.1\times {10}^2=10$ $m/s^2$