One end of a horizontal string is attached to a small- amplitude mechanical 60.0-Hz oscillator. The string's mass per unit length is 3.2 x10 kg/m. The string passes over a pulley, a distance = 1.50 m away, and weights are hung from this end. Assume the string at the oscillator is a node, which is nearly true. (Figure 1) Figure < 1 of 1
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- Final Answer must be decimal or whole number only!!!Problem 1: A simple harmonic oscillator is composed of a mass hanging from a spring. The mass of the hanging object is 400 g and the spring constant is 0.8 2. At the time t = 0 s, the mass is 2cm above its equilibrium position. The т amplitude of the oscillation is 5 cm. a) What is the initial phase? b) Find one of the times where the mass is located at 3cm above equilibrium. c) Find the kinetic and potential energies at t = 1s. d) What is the maximum kinetic energy?If the frequency of the motion of a simple harmonic oscillator is increased by a factor of 4, by what factor does the maximum speed of the oscillator change? 1/4 O It does not change. 04 02 O 1/2
- A block of mass m = 6.04 kg is attached to a spring with spring constant k = 1532 N/m and rests on a frictionless surface. The block is pulled, stretching the spring a distance of 0.145 m, and is held still. The block is then released and moves in simple harmonic motion about the equilibrium position. (Assume that the block is stretched in the positive direction.) (a) What is the frequency of this oscillation? Hz(b) Where is the block located 3.24 s after it is released? (Give the displacement from the equilibrium. Include the sign of the value in your answer.) m(c) What is the velocity of the mass at that time? (Indicate the direction with the sign of your answer.) m/sIf the object-spring system is described by x = (0.335 m) cos (1.65t), find the following. (a) the amplitude, the angular frequency, the frequency, and the period rad/s Hz (b) the maximum magnitudes of the velocity and the acceleration m/s max amax m/s² (c) the position, velocity, and acceleration when t 0.250 s m. m/s m/s2Harmonic Oscillator: 1.5kg object is connected to a spring with k=100N/m. (assume that there is no friction) If the object is pulled 3cm from equilibrium position, What will be the velocity of the object when the displacement from the equilibrium position is 2cm?
- A small bird's wings can undergo a maximum displacement amplitude of 4.50 cm (distance from the tip of the wing to the horizontal). If the maximum acceleration of the wings is 34.7 m/s^2, and we assume the wings are undergoing simple harmonic motion when beating, what is the oscillation frequency of the wingtips? ____________HzA simple harmonic motion is give by y = 12m * cos(8t) . What is the maximum acceleration in m/s^2?Answer A and B.
- A particle oscillates according to x = Acos(ωt + δ) Determine the phase constant δ if the particle starts from x0 = −A.Suppose that you start procedure step 6 with an initial string-length, Li = 30 cm, and finish with a final length, Lf cm. In this process of going from Li to Lf , the linear frequency of the pendulum decreases such that we find: (fi − ff ) fi × 100 = 34, where fi is the frequency of the pendulum at Li and ff is its frequency at Lf . What is the value of Lf ?A loudspeaker diaphragm is oscillating in a simple harmonic motion described by the equation d=acos(ωt) with a frequency of 614 Hertz (cycles per second) and a maximum displacement of 1.50 millimeters. Find ω and then determine the equation that describes the movement of the diaphragm.