A mass m oscillates on a spring with spring constant k, with amplitude d. At the moment when the mass is at position x = d/2, and moving in the +x direction (let this be when t = 0), a second mass 2m falls onto the first mass from above and sticks to it. Momentum is conserved in the x direction, but energy is not. (c) Write an expression for the energy lost in the collision in terms of d and k. (d) If after the collision the oscillator is subject to a damping force -bv and a drive force F0cos(ωt), find the drive frequency (in terms of the natural frequency ω0) which will return the oscillator to the original amplitude d.

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,