The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad / s . The frequency of this simple harmonic oscillator is _ _ _ _ Hz. [ . take . = 22 7 ]

Step-by-step solution

In a simple harmonic oscillator, if the displacement is x = A ( t + ) , the velocity is v = A ( t + ) . The kinetic energy is given by K = 1 2 mv^2 = 1 2 m A^2 ^2 ^2( t + ) . Using the identity ^2 = 1 + 2 2 , we get K = 1 4 m A^2 ^2 [1 + (2 t + 2 )] . The angular frequency of the kinetic energy oscillation is _ KE = 2 , where is the angular frequency of the SHM. Given _ KE = 176 rad/s, we have 2 = 176 , which gives = 88 rad/s. The frequency of the simple harmonic oscillator is f = 2 . Substituting the values: f = 8