5) A mass m is attached to a spring of force constant 75.0N/m and allowed to oscillate. The figure below shows a graph of its velocity v as a function of time t. (a) Find the period, (b) Find the frequency and (c) the angular frequency of this motion (d) What is the amplitude (in cm) and at what times does the mass reach this position? (e) Find the maximum acceleration of the mass and the times at which it occurs. (f) What is the lass m? SHO: Mass-spring: @= ax(t) = ²x=-w²x(t) x(t) = A cos(wt + p) m Simple pendulum: T = 2π w = 2nf= = ²/F vx (cm/s) Vx 20 10 -10 -20 11 126) 0.2 0.6 1.0 1.4 1.8

In the experiment, you will study an oscillator called a "torsion pendulum." In this case, the restoring "force" is the torsion constant of the wire that suspends the weight X and the inertial term is the rotational inertia of the suspended mass. You will compare the periods of a suspended sphere and of a suspended cube. The rotational inertia of a sphere is Is = 1/10msD^2, where ms is the mass of the sphere and D is its diameter. The rotational inertia of a cube is Ic = 1/6mcS^2, where mc is the mass of the cube and S is the length of its side. If the cube and the sphere are suspended from the same wire, what is the expected ratio of their periods, Tc/Ts? Assume that D = S, ms = 0.20kg, and mc = 0.5 kg.

A block is tied to a spring and is oscillating with an amplitude of A = 16 cm. The angular frequency w = 6 rad/s. What is the maximum acceleration of the block?

A solid cylinder of mass M and radius R is mounted to an axle through its center. The axle is attached to a horizontal spring of constant k, as shown in the figure. Initially the cylinder is at rest and the spring is un-stretched. The cylinder is then pulled a distance A and released. The cylinder rolls back and forth without slipping. A) Determine the angular frequency ωfreq and period T of the simple harmonic motion of this spring-rolling mass system? Express your answer in terms of k and M. B) Assume that we have the same spring and mass system, onlynow the cylinder is released from rest on a frictionless surface at a distance A from the equilibrium position. What is the period of the simple harmonic motion of this system? Express your answer in terms of k and M.