Compute and plot the response for the system illustrated in

Compute and plot the response for the system illustrated in Figure P3.9 for the input force also shown. You\'ll note that the second harmonic (2_omega_0 = 1.57) is very close to the system\'s natural frequency. Since the damping is equal to zero, why isn\'t this harmonic dominating the response?

Solution

The eqn for the oscillator without damping is the same as the usual except for the spring constant

so mx\' + (k1-k2)x =f(t)

Where f(t) is the forcing function.

Analytically, for a forcing function whose graph is known, the Laplace or Fourier transforn gives a solution.

The shown function does not have any amplitude value,but take it as 1

Take the inverse transform withthe forcing function and you get the result.

Other method use MATLAB.

Best

The natural frequency is ( for only k1) .8 and for the combined springs 1.13