2. An object is in damped SHM. Initally is it at x=0m and v=3m/s. The mass is 4kg, the spring constant is 36 N/m and the damping constant is C=8V5 in the usual units. Find an expression for x(t) and vſt).
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- b. An object with a mass of 0.2 kg attached to a spring exhibits simple harmonic motion according to the equation x = 0.04 cos ( 20zt +"). Find the frequency and the period of the oscillation. Find the velocity of the particle, its acceleration and the acting force, as well as the amplitudes of the respective quantities. wwwip Figure 3: Question 2(b) A spring mass systemA particle with a mass of 0.1 kg undergoes SHM with an amplitude of 0.05 m. Its maximum acceleration is 10g, where g stands for the gravitational acceleration. What is the period of the oscillation? What is the maximum speed of the particle? What is the total mechanical energy of the particle? What is the magnitude of the force on the particle when it is at 1/3 of its maximum displacement? 2.The period of motion of an object-spring system is T = 0.606 s when an object of mass m = 278 g is attached to the spring. (a) Find the frequency of motion in hertz. Hz(b) Find the force constant of the spring. N/m(c) If the total energy of the oscillating motion is 0.254 J, find the amplitude of the oscillations. m
- 6. A 2.0 kg mass attached to a 24.0 N/m massless spring is driven by an external force F = F, cos (2nt) where Fo= 12.0 N. Assuming that the damping coefficient b is so small that it can be neglected, find a) the period of the oscillator, and b) the amplitude of its motion.A small mass m is attached to a string of length L to make a simple pendulum that swings with period T. Suppose the mass is cut in half, what might the new period of oscillation be? Α. 2T T В. С.Т D. V2T An alien on Pluto has the exact same pendulum. What is the period of oscillation of the alien's pendulum in terms of T, given that the acceleration due to gravity on Pluto is 1/16 of the acceleration due to gravity on Earth? TPlutoEnergy (J) 20 PE 15 10- 10 5 12 16 20 24 24 28 25 . Suppose the damping constant b of an oscillator increases. a. Is the medium more resistive or less resistive? b. Do the oscillations damp out more quickly or less quickly? c. Is the time constant 7 increased or decreased? TE x (cm)
- 2. The length of a simple pendulum is 0.66 m, the pendulum bob has a mass of 310 g, and it is released at an angle of 12º to the vertical a. With what frequency does it oscillate? Assume SHM.5. 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.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.