**4.30. No damping force**A particle of mass \( m \) is subject to a spring force, \(-kx\), and also a driving force, \( F_d \cos \omega_d t \). But there is no damping force. Find the particular solution for \( x(t) \) by guessing \( x(t) = A \cos \omega_d t + B \sin \omega_d t \). If you write this in the form \( C \cos(\omega_d t - \phi) \), where \( C > 0 \), what are \( C \) and \( \phi \)? Be careful about the phase (there are two cases to consider).

By dissipating energy, damping forces are used to restrain vibrating motion, for example,…

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