Simple harmonic motion: The simple harmonic motion of an object is described by the graph shown in the figure. What is the equation for the position x(t) of the object as a function of time t? 4. 54321 x (cm) A AS + + +∞ -1 2 3 4 5 6 7 8 -2 9 10 11 12 13 14 15 16 17 t(s) -3 -4.

The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in radians and = 4.43 rad/s. Determine the period and length of the pendulum.

An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, what is the period of the motion? (a) 2T (b) 2T (c) T (d) T/2 (e) T/2

Period of a pendulum A standard pendulum of length L that swings under the influence of gravity alone (no resistance) has a period of T = 4 (/2 dọ w Jo Vi- k sin²o where o = g/L, k? = sin² (8,/2), g = 9.8 m/s² is the acceleration due to gravity, and 0, is the initial angle from which the pendulum is released (in radians). Use numerical integration to approximate the period of a pendulum with L = 1 m that is released from an angle of 0, = 7/4 rad. %3D

A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 2л√m/k, wherek is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? O [T] O [M] O [M]/[T] O [T]/[M] O [M]/[T]² O [T]²/[M]

Juan wants to know the height of a museum. Inside the museum, he notices a very long simple pendulum extending from the ceiling and almost touching the floor. Remembering his lessons in physics, he realizes that he can estimate the height of the museum from the period of the pendulum's oscillation. If the pendulum undergoes one complete oscillation in 21.28 seconds, how tall is the tower? Round off your final answer to two decimal places. Add your answer

Problem 3:  The frequency of oscillation of a pendulum on a different planet is 3.3 Hz, and the acceleration due to gravity is 290 m/s2 Calculate, in meters, the length of the pendulum.

O 0.15 sec In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is Tt s^(-1). What is the time needed for the pendulum to complete two oscillations? O 1 sec O 2 sec O 4 sec O 0.5 sec O 0.25 sec

An object oscillates with simple harmonic motion along the x-axis. Its displacement from the origin varies with time according to the equation =4cos(7nt+r/3)m. Where t is in seconds and the angles in the parentheses are in radians. 1. the amplitude is m. 2. the angular frequency (w) is 3. the frequency(f) = rad/s, Hz. 4 the period (T) = 5. the x-position at t=Os is m 6, the maximum speed = m/s 7. the maximum acceleration = m/s2 B. Att = 1s. the displacement x = m 9. Att =1s, the velocity is m/s 10 At t= 1s. the acceleration is m/s

Consider the pendulum shown at the right. It has the following characteristics: . T = 1.45 s • m = 0.250 kg Answer the three parts below, using three sig figs. 1 m