child with mass of 10 kg gets into a toy car with mass of 65 kg on a playground, causing it to sink on its spring (with spring constant 327 N/m). An adult walks by and gives the top of the car a shove, causing it to undergo oscillations with amplitude 30 cm in the vertical direction. Assuming the oscillations are simple harmonic, what is the angular frequency of the oscillations? ω = (in rad/s) a. 0.673 b. 1.715 c. 2.088 d. 2.243

On a nice spring day you find yourself relaxing under an old oak tree. You pull the end of one of the tree's branches down (negative maximum displacement) about 2 ft and let it go (t = 0 s). You note that the resulting motion appears to be from a simple harmonic oscillator with a period of about 2.5 seconds. It takes the branch about 8 oscillations to decrease the amplitude by a factor of 2. (a) What evidence could you have to claim the branch undergoes simple harmonic motion? (be brief) (b) Describe the energy transfers in the branch + earth system during an entire cycle of the motion. Focus on the three most important types of energy in the system. Feel free to use a plot or diagram to illustrate how/ when the energy changes forms. (c) What is the time constant τ for the amplitude as a function of time during the damping of the oscillation.

Calculate the velocity of a simple harmonic oscillator with amplitude of 13.5 cm and frequency of 5 Hz at a point located 5 cm away from the equilibrium position. Give your answer in Sl units.

a) Use energy conservation to find the amplitude of the motion. b) Use energy conservation to find the maximum speed of the glider.   c) What is the angular frequency of the oscillations?      (express in rad/s)

a particle of mass m makes simple harmonic motion with force constant k around the equilibrium position x = 0. Calculate the valu of the amplitude and the phase constant if the initial conditions are x(0) = 0 and v(0) = -Vi (vi > 0). Draw x-t, v - t and a - t figures for one complete cycle of oscillations.

A simple pendulum has a mass of 0.450 kg and a length of 5.00 m. It is displaced through an angle of 13.0° and then released. Using the analysis model of a particle in simple harmonic motion, calculate the following. (Give your answer to the thousandths place.) (b) What is the maximum angular acceleration of the bob?

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 uniform stick of length L and mass m is pivoted at one of its ends. Derive an equation for the period of oscillation when the stick is set into small oscillation. Answer in terms of m, g, and L as needed.

Pr5. A pointlike body of mass m made of lead is fixed inside a homogeneous solid sphere of radius R and mass m at distance R/2 from the center of the sphere. This body is placed on a horizontal rough surface. Find the period of small oscillations of the sphere around its equi- librium position. (The sphere rolls without slip- ping on the surface. The moment of inertia of a homogeneous sphere of mass m and radius R is 2mR* /5.) R/2

The figure shows a uniform rod (length L = 2.36 m, mass = 1.9 kg) suspended from a pivot a distance d = 0.27 m above its center of mass. The angular frequency (in rad/s) for small oscillations is: axis