A mouse, mass m,, sits on the bob of the pendulum, mass m,. The length of the pendulum string is 1. The mouse jumps horizontally with a velocity of magnitude v,. Assume that the mouse jumps so quickly that the string remains vertical during the impact. a) Find the velocity of the bob right after the mouse's jump. //// Vo ту тp b) Derive the equation that could be solved to find the dependence 0(t), where 0 is an angle the string makes with vertical, if the displacement is small (sin 0~ 0). c) Find 0(t). How long will it take for the pendulum to return to the equilibrium?
A mouse, mass m,, sits on the bob of the pendulum, mass m,. The length of the pendulum string is 1. The mouse jumps horizontally with a velocity of magnitude v,. Assume that the mouse jumps so quickly that the string remains vertical during the impact. a) Find the velocity of the bob right after the mouse's jump. //// Vo ту тp b) Derive the equation that could be solved to find the dependence 0(t), where 0 is an angle the string makes with vertical, if the displacement is small (sin 0~ 0). c) Find 0(t). How long will it take for the pendulum to return to the equilibrium?
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Transcribed Image Text:A mouse, mass m,, sits on the bob of the pendulum, mass m,. The length of the pendulum string is
1. The mouse jumps horizontally with a velocity of magnitude v,. Assume that the mouse jumps
so quickly that the string remains vertical during the impact.
a) Find the velocity of the bob right after the mouse's jump.
////
Vo
ту
тp
b) Derive the equation that could be solved to find the dependence 0(t), where 0 is an angle the string
makes with vertical, if the displacement is small (sin 0~ 0).
c) Find 0(t). How long will it take for the pendulum to return to the equilibrium?
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