The graph below shows the angular position as a function of time for a simple pendulum that is oscillating in a gravitational field with g=9.81m/s^2 Part a) calculate the amplitude in radians Part b)find the equation for the angular position as a function of time theta(t). Part c) find the equation for the angular velocity as a function of time omega(t).

For a simple pendulum, the restoring "force" is the torque due to gravity, mgL. Here m is the mass of the pendulum, g is the acceleration due to gravity, and L is the length of the pendulum. The "inertia" is the rotational inertia, mL². What is the expected period T of a simple pendulum? OA. 2л√/mg/L OB. 2√✓/L/mg OC. 2n√L/g OD. 2n√g/L OE. none of these

A point rotates about the origin in the ?? plane at a constant radius of 0.211 m with an angular velocity of 9.01 rad/s. The projection of this point's motion on the ?- or ?-axis is simple harmonic. What is the amplitude of the projected simple harmonic motion? What is the projected motion's frequency? What is the projected motion's period?

Ferris Wheel The height h (in feet) above groundof a seat on a Ferris wheel at time t (in seconds) ismodeled byh(t) = 53 + 50 sin(π10t − π2).(a) Find the period of the model. What does the periodtell you about the ride?(b) Find the amplitude of the model. What does theamplitude tell you about the ride?(c) Use a graphing utility to graph one cycle of the model.

PRACTICE IT Use the worked example above to help you solve this problem. A 0.545 kg object connected to a light spring with a spring constant of 19.0 N/m oscillates on a frictionless horizontal surface. (a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm. E = J m/s V max = (b) What is the velocity of the object when the displacement is 2.00 cm? ± m/s (c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm. KE = J J PES= EXERCISE For what values of x is the speed of the object 0.14 m/s? x = ± cm HINTS: GETTING STARTED I I'M STUCK!

The equations used to describe the physical pendulum will lead us directly to an answer. Part 3 of 3 - Analyze We are givenf = 0.685 Hz, d 0.510 m, and m = 2.10 kg. We have the following equation for the period. T = 2n V mgd This gives 4721 T2 = mgd and, solving for the moment of inertia, we have the following. T?mgd mgd %3D kg )(9.80 m/s?) m Hz kg - m2 Submit Skip (you cannot come back) Need Help? Read it O Show My Work (Optional) ?