Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) (b)Write an equation that represents the curve in the form

A solid cylinder of mass M, radius R, and length L, rolls around a light, thin axle at its center. The axle is attached to a spring of stiffness K on either side. The springs are attached to same wall. The cylinder is brought back a distance A, parallel to the wall, and allowed to oscillate. What is the maximum speed of the oscillations of the cylinder? Answer: ((3*k*A^2)/(2*M))^1/2

An object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.1 cos(3.4t – 1.9), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians. Find the amplitude of the simple harmonic motion, in meters.  What is the value of the angular frequency, in radians per second?  Determine the position of the object, in meters, at the time t = 0.  What is the object’s velocity, in meters per second, at time t = 0?  Calculate the object’s acceleration, in meters per second squared, at time t = 0.  What is the magnitude of the object’s maximum acceleration, in meters per second squared?

Consider the simple pendulum: a ball hanging at the end of a string. Derive the expression for the period of this physical pendulum, taking into account the finite size ball (i.e. the ball is not a point mass). Assume that the string is massless. Start with the expression for the period T'of a physical pendulum with small amplitude oscillati T = 2π The moment of inertia of the ball about an axis through the center of the ball is Here, I, is the moment of inertia about an axis through the pivot (fixed point at the top of the string, m is the mass of the ball, g is the Earth's gravitational constant of acceleration, and h is the distance from the pivot at the top of the string to the center of mass of the ball. Note, this pre-lab asks you to do some algebra, and may be a bit tricky. I mgh Iball = / mr² T