Question

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 9.8 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?a. 4.6 Hz b. 1.4 Hz c. 2.3 Hz d. 3.2 Hz

Answer 1

7.04 Hz

Step-by-step explanation:

x(t) = A cos(wt)

v(t) = - wA sin (wt)

Vmax = wA

E = 1/2 * m * (Vmax)^2

E = 1/2*m*(wA)^2

`w = (1)/(A) \sqrt{(2E)/(m) }`

f = w/ 2*pi

`f = (1)/(2*pi*A)*\sqrt{(2E)/(m) } \\f = (1)/(2 * pi * 0.2)*\sqrt{(2(9.8))/(0.25) } \\f = 7.04 Hz`