2. A 0.8 kg block is attached to horizontal spring. The system is set into motion by pushing the block 15.0 cm to the left of the equilibrium position and then released. The resulting frequency of oscillation is 2.5 Hz. Determine a) the angular frequency b) the spring constant c) expressions for the displacement, velocity and acceleration as functions of time d) displacement, velocity, acceleration, kinetic energy, elastic potential energy, and restoring force at t=1.48 s
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- 3. A simple harmonic oscillator consists of a block attached to a spring with k = 200 N/m. The block slides on a frictionless surface, with equilibrium point x = 0 and amplitude 0.20 m. A graph of the block's velocity v as a function of time t is shown. The horizontal scale is set by t, = 0.20 s.What v (m/s) t (s) are -2n the period of the SHM the block's mass а. b. it's displacement at t = 0 it's acceleration at t = 0.10 s, and it's maximum kinetic energy? С. d. е.2. Dr. Benton has long thought that OSU should install a Foucault (simple) pendulum in the atrium of the Nobel Research Center. Let us consider how such a pendulum might function. Assume that the pendulum bob had a mass of 22 kg and was suspended from a thin 12 m long chord. Also, assume that the circular area over which the pendulum would swing was 4.9 m². Determine a) the period of the pendulum, and b) the maximum velocity of the pendulum bob.2. A 100 gram mass is attached to a spring and undergoes simple harmonic motion with period of T=2 sec. If the total energy of the systenm is E= 5J, find (a) force constant k. and (b) the amplitude of motion 4.
- 2. An object whose mass is 520 g is fastened to the end of a horizontal spring whose spring constant is 78 N/m. The object is pulled 5.0 cm from equilibrium and released. Assume no friction between the object and the floor. (a) What is the angular frequency and the period of oscillation? b) Write the specific equation of motion for this oscillating system, in the form x(t) A cos(cot + )5. A block of mass of 500 grams is attached to a spring of constant k = 400 N/m. The oscillation frequency is 8.00 Hz. Determine (a) the angular frequency, (b) the period, and (c) the force on the spring if its maximum displacement is 8.5 cm.5) A 750 gr block is fastened to a spring with a spring constant of 145 N/m and then pulled 25 cm and released on a horizontal frictionless surface. a) What is the frequency of the motion? b) What is the Period of the motion? c) What is the angular frequency? d) What is the Amplitude? e) Write an equation of the Position as a function of time. f) Write an equation of the Velocity as a function of time. g) Write an equation of the Acceleration as a function of time. h) What is the maximum velocity? i) What is the maximum acceleration?
- 7. In a lab experiment, you are given a spring with a spring constant of 14 N/m. What mass would you suspend on the spring to have an oscillation period of 0.93 s when in SHM? kg5. A block is attached to a horizontal spring. Find a model for the displacement d as a function of time given the following conditions: a. At time t = 0, the block is pulled to the left 6 cm with a frequency of 2 Hz. W -3-2-1 0 1 2 3 + d b. At time t = 0, the initial displacement is 0 inches (moving to the right), the amplitude is 15 centimeters, and the period is 1 sec.Q2.A physical pendulum consists of a ring of radius 0.5 m and mass 2 kg. The ring is pivoted at a point on its perimeter. The ring is pulled out such that its centre of mass makes a small initial angle ?0 = 0.2 rad from the vertical and released from rest. (C) Calculate the angular frequency of the oscillation of the ring (D) Calculate the period of the oscillation of the ring
- 3. A mass on a spring moving along the x-axis in simple harmonic motion starts from the equilibrium position, the origin, at t = 0 and moves to the right (consider the right to be the positive x direction). The amplitude of its motion is 3.00 cm and the frequency is 1.50 Hz. At what earliest time does this mass have the maximum positive acceleration (i.e.pointing in the positive x direction)? X = 0 +x a. t= 0.500 seconds. b. t= 0.667 seconds. Ax с. t = = 1.50 seconds. d. t= 0.167 seconds. e. t= 0.314 seconds.1. A grandfather clock is constructed so that it has a simple pendulum that swings from one side to the other, a distance of 30.1 mm, in 1.00 s. what is the maximum speed of the pendulum bob?