Question

An oscillating mass spring system has a mechanical energy 1 Joule, when it has an amplitude 0.1m and maximum speed of 1 m$s^{-1}$. Then the force constant of the spring is

• A. 100 N$m^{-1}$
• B. 200 N$m^{-1}$
• C. 300 N$m^{-1}$
• D. 50 N$m^{-1}$

Answer 1

Answer: (B)

200 N$m^{-1}$

$V_{max}=wA=1m/s$
$A=0.1m$
$\frac{1}{2}m{w}^2{A}^2=1J$
$m{w}^2{A}^2=2$
$m{w}^2(A\times A)=2$
$m{w}^2=\frac{2}{0.1\times 0.1}=200N/M$