Question

The variation of PE of a simple harmonic oscillator is as shown. Then force constant of the system is (PE 'U' is in joules, displacement ${}^{\prime }{x}^{\prime }$ is in mm)

• A. $\text{100 N/m}$
• B. $\text{150 N/m}$
• C. $\frac{200}{3}\text{N/m}$
• D. $\text{300 N/m}$

Answer 1

The correct option is B $\text{150 N/m}$

Given,

$A=20mm$

$U_{min}=0.01J$

$U_{max}=0.04J$

The change in potential energy is given by

$U_{max}-U_{min}=\frac{1}{2}k{A}^2$

$0.04-0.01=\frac{1}{2}k(20\times {10}^{-3}{)}^2$

$0.03=2k\times {10}^{-4}$

$k=\frac{0.03}{2\times {10}^{-4}}=\frac{0.03\times 10000}{2}=\frac{300}{2}$

$k=150N/m$

The correct option is B.