Q2. The motion of a damped mass and spring system can be described by the equation \( m x^{\prime \prime}+\gamma x^{\prime}+k x=F(t) \). Find the transient and steady periodic oscillation of the system by using method of undetermined coefficient. Choose the value for mass, damping and spring constant \( m=1 \mathrm{~kg}, \gamma=3 \), and \( k=2 \mathrm{~N} / \mathrm{m} \) under the influence of an external force \( F(t)=5 \cos (4 t) \) with \( x(0)=0 \) and \( x^{\prime}(0)=0 \). Explain the result. (12M)
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The initial conditions are \( x(0)=0 \) and \( x^{\prime}(0)=0 \). Show more…
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