An 85.0 kg mountain climber plans to swing down, starting from rest, from a ledge using a light rope 6.50 m long. he swings from an initial angle of θ0=−10∘ with respect to the vertical. in this case, assume that the angle is small enough to approximate the motion as simple harmonic motion. use g=9.8m/s2.
a) solve for the period of the oscillation of the climber.
b) how long will it take the climber to first reach the lowest point in the swing (θ=0∘)?
c) write an equation for the angle of the pendulum with respect to the vertical as a function of time. remember to solve for the phase constant properly.
your answer should be in the form θ(t)=acos(ωt+ϕ) as usual.
d) solve for the angle of the rope at t=1.28s. check that your answer agrees with your answer to part (b).