Consider an unknown mass m fixed to a spring with spring constant k = 22.7 N/m. It is compressed to a maximum displacement from its equilibrium position by Dxi = 0.378 m as shown in the figure below. The spring and mass are then released and the mass is allowed to oscillate on a frictionless surface. It is observed to complete 11.0 oscillations in 18.5 s. What is its angular frequency of oscillation? What is the mass m fixed to the spring? What is the elastic potential energy stored in the spring when the mass is at its maximum displacement Dxi = 0.378 m? What will the speed of the mass be when it crosses the spring’s equilibrium position?

A particle undergoes simple harmonic motion with angular velocity of 3.0 rad/s and amplitude of 0.5 m. It starts with maximum forward displacement at time t = 0. Find the velocity at time t = 2.0 s

In the figure, a solid cylinder attached to a horizontal spring (k = 5.80 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.290 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 6.20 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) M · k oooooo (a) Number i 0. (b) Number i (c) Number i O. Units Units Units

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

In the figure, a solid cylinder attached to a horizontal spring (k = 9.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 5.30 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) (a) Number i Units (b) Number i Units (c) Number i Units >

An object oscillates with an angular frequency ω = 6 rad/s. At t = 0, the object is at x0 = 1.5 cm. It is moving with velocity vx0 = 14 cm/s in the positive x-direction. The position of the object can be described through the equation x(t) = A cos(ωt + φ). What is the the phase constant φ of the oscillation in radians?  Write an equation for the amplitude A of the oscillation in terms of x0 and φ. Use the phase shift as a system parameter.  Calculate the value of the amplitude A of the oscillation in cm.

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.

A thin uniform rod (mass = 0.24 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.1 s and an angular amplitude of 9.6°. (a) What is the length of the rod? (a) What is the maximum kinetic energy of the rod as it swings?

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

A thin uniform rod (mass = 0.19 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.6 s and an angular amplitude of 6.3°. (a) What is the length of the rod? (a) What is the maximum kinetic energy of the rod as it swings? (a) Number i Units (b) Number i Units