A mass weighing 8lbs is attached to a spring suspended from a ceiling. When the mass comes to rest at equilibrium, the spring has been stretched 6 in. The mass is then pulled down 3 in. below the equilibrium point and given an upward velocity of 0.5 ft/sec. Neglecting any damping or external forces that may be present, determine the equation of motion of the mass, alone with its amplitude, period, and natural frequency. Sketch the graph of this simple harmonic motion.
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- An object weighing 32 lb stretches a spring 2ft in equilibrium. There is also a damping force with c = 8. The spring is raised 2 ft and thrown upwards with a velocity of 4ft/sec. Determine the mass m and the spring constant k, and give the differential equation describing the harmonic motion of this system. Solve the differential equation to find the displacement y.An object of mass 0.4 kg at the end of a spring is released at an initial height of h = 0.494 m relative to the equilibrium position, and with initial velocity 1.003 m/s. After it is released, the object oscillates at 2 rad/s. a. Find the amplitude of the oscillation b. Find the phase constant 4, where x(t) = A cos (wt + p) c. What is the acceleration at t=0? d. What is the total energy of the system?A 1.3 kg block is attached to a spring with spring constant 13 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 39 cm/s. Part A: What is the amplitude of the subsequent oscillations? Part B: What is the block's speed at the point where x=0.40 A?
- A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.80 Hz. Block B rests on it, and the coefficient of static friction between the two is µ. = 0.640. What maximum amplitude of oscillation can the system have if block B is not to slip? cm Ms POn a nice spring day you find yourself relaxing under an old oak tree. You pull the end of one of the tree's branches down (negative maximum displacement) about 2 ft and let it go (t = 0 s). You note that the resulting motion appears to be from a simple harmonic oscillator with a period of about 2.5 seconds. It takes the branch about 8 oscillations to decrease the amplitude by a factor of 2. (a) What evidence could you have to claim the branch undergoes simple harmonic motion? (be brief) (b) Describe the energy transfers in the branch + earth system during an entire cycle of the motion. Focus on the three most important types of energy in the system. Feel free to use a plot or diagram to illustrate how/ when the energy changes forms. (c) What is the time constant τ for the amplitude as a function of time during the damping of the oscillation.You have a simple pendulum that consists of a small metal ball attached to a long string. You push the ball so that at time t=0 it moves with a speed of 0.62 m/s through the equilibrium in the negative x-direction and continues oscillating with amplitude 16 cm. (a) Draw labeled position-time and velocity-time graphs for the first two periods of oscillation. (b) Determine the length of the string. 1. Draw a sketch of the situation, labeling all of the physical quantities given in the problem. Identify system in the sketch. 2. Draw a force diagram showing the forces exerted on the pendulum at its maximum amplitude and position-time and velocity-time graphs showing two full oscillations of the pendulum's motion.
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- You are sitting on a surfboard that is riding up and down on some swells. The board’s vertical displacement is given by Y = (1.2m)cos((t)(1/2s) +π/6) Find amplitude, angular frequency, phase constant, frequency, and period of the motion. Where is the surfboard at t = 1.0s? Find the velocity and acceleration as functions of time t. Find the initial values of the position, velocity, and acceleration of the surfboard.A driving force of the form F (t) = (0.260 N) sin (27 ft) acts on a weakly damped spring oscillator with mass 5.63 kg, spring constant 373 N/m, and damping constant 0.163 kg/s. What frequency fo of the driving force will maximize the response of the oscillator? fo = Hz Find the amplitude A, of the oscillator's steady-state motion when the driving force has this frequency. Ao = about us privacy policy terms of use contact us help careersA 0.950 kg block is attached to a spring with spring constant 17.0 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 35.0 cm/s. What is the amplitude of the subsequent oscillations? What is the block's speed at the point where x=0.50A?