A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes at distance r from the axle. Assuming that the wheel is a hoop of mass m and radius R, what is the angular frequency w of small oscillations of this system in terms of m, R, r, and the srping constant k? What is w if r =R and if r = 0?

You have a metal spring of negligible mass that has spring constant k. The spring is supporting an object of mass m which is oscillating up and down with an angular frequency of w. What happens when a large steady current passes through the spring? O The oscillations gradually slow down until they come to a complete stop O The mass continues to oscillate with a reduced oscillation period O The mass continues to oscillate with an increased oscillation period O The mass continues to oscillate with the same oscillation period

You have made a physical pendulum by swinging a rod of mass M = 1.08 kg and length L = 1.45 meters around its end. The mass of the rod is distributed uniformly along its length. We will assume that the amplitude of the swing is max = 19.34 degrees. Solid Rod Swings in Simple Harmonic Motion ^ 0=-0, max 0=+0₁ max Determine all the following: The FORMULA for the moment of inertia of your rod, I = The distance from the pivot point to the Center-Of-Mass, d = The angular frequency of the pendulum, w = The amplitude of the motion in radians, max = radians The angular velocity when 0 = 64% of full swing, w(0 = 0.64 0max): NOTE: The first question requires a FORMULA, not a value. rad/sec = meters rad/sec

A small block with mass m slides along a frictionless horizontal surface with a speed v = with and sticks to the end of a uniform rod (mass M = m, length L = 0.75 m) that can rotate around a frictionless axle through its upper end as shown. :0.4 m/s. It collides %3D a) Use Newton's 2nd law to find the angular frequency w of small angle oscillations for the combined system. b) What is the amplitude (maximum displacement 0max) from the vertical, expressed in degrees?