Problem 5: (a) For a driven, damped harmonic oscillator, the peak of the amplitude (and therefore the maximum potential energy) occurs for a driving frequency of w = ₂ = √w – 2/3². Determine the driving frequency at which the kinetic energy of the system is a maximum. (b) Make a "resonance peak" plot of kinetic energy versus driving frequency, for various values of ß. [You may assume that wo = 1 rad/s, or equivalently you can choose to measure driving frequency w and damping ß as fractions or multiples of wo. Choose a convenient value for the driving force.]

Can you show me how to solve this?

An object stretches a spring 6 centimeters in equilibrium. Find its displacement for t>0 if it is initially displaced 3 centimeters above equilibrium and given a downward velocity of 6 centimeters/sec. Assume that there’s no damping.

A block of mass m = 3kg is attached to a light spring with a spring constant k and moves in simple harmonic motion on a frictionless horizontal surface. Initially the spring is compressed to x, = -–0.1 m from its equilibrium position and is given an initial velocity vo in the negative x-direction, as shown in the figure below. The maximum speed reached by the block is vmax = v2 m/s. The block's period of oscil- lation is T= 0.889s. 3) The velocity of the block att = 0, vo is: hmmo Equilibnura aV2 m/s b. V2 m/s e. -1 224 m/s d 1224 m/s www