Question

For any SHM, amplitude is $6cm$. If instantaneous potential energy is half the total energy then distance of particle from its mean position is

• A. $3cm$
• B. $4.2cm$
• C. $5.8cm$
• D. $6cm$

Answer 1

Answer: (B)

$4.2cm$

The potential energy in SHM is given by ,

$U=1/2k{y}^2$

where , $k=$ force constant

$y=$ distance of particle from mean position

Total energy in SHM is given by ,

$E=1/2k{a}^2$

where, $a=$ amplitude in SHM

given , $U=E/2$

$1/2k{y}^2=\left(1/2\right)\left(1/2\right)k{a}^2$

or $y^2=a^2/2$

now , given that $a=6cm$ ,

Hence, $y^2=6^2/2=18$

or $y=\sqrt{18}=4.2cm$