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. (a) Write an equation that describes the motion x(t) of the mass m before the collision. (b) Write an equation that describes the motion x(t) of the combined masses after the collision.
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.
(a) Write an equation that describes the motion x(t) of the mass m before the collision.
(b) Write an equation that describes the motion x(t) of the combined masses after the collision.
(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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