A linear harmonic oscillator of force constant 2 × 106 N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Show that its (a) maximum potential energy is 160 J (b) maximum kinetic energy is 100J

Question

A linear harmonic oscillator of force constant 2 × 106 N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Show that its (a) maximum potential energy is 160 J (b) maximum kinetic energy is 100J (A) P.E. is 160 J (B) P.E. is zero (C) P.E. is 100 J (D) P.E. is 120 J

Tardigrade Admin · Accepted Answer

Force constant (k)=2 × 106 N / m; Amplitude (x)=0.01 m and total mechanical energy =160 J. Potential energy =(1/2) k x2=(1/2) ×(2 × 106) ×(0.01)2 =100 J.

Q. A linear harmonic oscillator of force constant $2 \times 1 0^{6}$ N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Show that its (a) maximum potential energy is 160 J (b) maximum kinetic energy is 100J

P.E. is 160 J

P.E. is zero

P.E. is 100 J

P.E. is 120 J

Force constant $(k) = 2 \times 1 0^{6} N / m$ ;
Amplitude $(x) = 0.01 m$ and total mechanical energy $= 160 J$ .
Potential energy $= \frac{1}{2} k x^{2} = \frac{1}{2} \times (2 \times 1 0^{6}) \times (0.01)^{2}$
$= 100 J$ .

Q. A linear harmonic oscillator of force constant 2×106 N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Show that its (a) maximum potential energy is 160 J (b) maximum kinetic energy is 100J