The governing differential equation of a forced harmonic oscillation of a damped mass-spring system is given by mx" + cx' + kx = p(t) where m is the mass, c is the damping coefficient, k is the spring coefficient and p(t) is the forcing function. For m = 1 kg, c = 6 kg/s, k = 45 N/m, p(t) = cos5t (N), x(0) = 0 and x'(0) = 0, find the oscillation of the system between 0-5s. Use Laplace transform in your solution. -x(1) ww m O p(1)

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.