Question

-The velocity of a simple harmonic oscillator is given by v = -7.93sin(29.4t) (mks units) What is its angular frequency?

-What is the amplitude of the motion in Problem 1 in meters to two decimal places?

-To the nearest hundredth of a meter where is the mass in Problem 1 at the time t = 22.64 seconds?

-If the mass in Problem 3 is 0.34 kg, what is the spring's potential energy to the nearest tenth of a joule?

-What is its kinetic energy to the nearest tenth of a joule?

Answer 1

The general equation for the simple harmonic oscillator is,

              v = -Awsinwt

here, A is amplitude, w is angular frequenct, and t is the time.

1.

The angular frequency is: 29.4 rad/s

2.

The amplitude of the oscillator is: A = 7.93 / w = 7.93 /29.4 = 0.2697 m = 0.27 m

3.

The general equation for the displaceemnt of the oscillator is,

         x = Acoswt = 0.27cos29.4*22.64 = 0.248 m

4.

The spring constant is,

              k = w²m = 29.4*29.4*0.34 = 293.8824 N/m = 294 N/m

potential energy is,

          PE = 0.5kx2 = 0.5*294*0.248*0.248 = 9.04 J

5.

The velocity is,

     v = -7.93sin(29.4t) = -7.93sin(29.4*22.64) = 3.1 m/s

The kinetic energy is,

                  K = 0.5mv2 = 0.5*0.34*3.1*3.1 = 1.63 J