A particle of mass moves in a 2-dimensional plane under the influence of a force spring (in figure) with initial position (b, 0) and initial velocity (0, v0) What is the period of the oscillation?
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A particle of mass moves in a 2-dimensional plane under the influence of a force spring (in figure)
with initial position (b, 0) and initial velocity (0, v0)
What is the period of the oscillation?
Step by step
Solved in 4 steps
- You may also recall that for a simple pendulum N = V, where g is the acceleration due to gravity and L is the length of the pendulum. This has been inserted in Equation 4 above. Lastly, this means that angular position 0 of the pendulum is given by: 0 = 0, cos(Nt) Equation 5 Question 1 Use the information above and Equation 2 to write an equation for the period of the pendulum in terms of g and L.A pendulum has a period of 5.8 s. If you were to transfer this pendulum to the surface of Mars (where g is 3.71 meters per second squared), what would the period (in seconds) be?A cylindrical disc with a mass of 0.619 kg and radius of 0.575 m, is positioned such that it will oscillate as a physical pendulum as shown below. If the period of the small angle oscillations is to be 0.343 s, at what distance from the center of the disc should the axis of rotation be fixed? Assume that the position of the fixed axis is on the actual disc. The moment of inertia of a disc about its center is 1 = 0.5 M R²...Hint: Use the parallel axis theorem.
- You will fire the spring gun 3 times from the first detent and measure the change in height of the (pendulum + ball) for each shot. Write the equation for the change in height of the first shot.The quantities A and φ (called the amplitude and the phase) are undetermined by the differential equation. They are determined by initial conditions -- specifically, the initial position and the initial velocity -- usually at t = 0, but sometimes at another time. In the oscillating part of the experiment, I measured only the time of 30 periods. I measured no position or velocity. Consequently, A and φ (and also y0) are irrelevant in the problem. We only compare the period T or the frequency ω with the theoretical prediction. You have (hopefully) derived (or maybe looked up) the relation between ω and k and m. This final question relates ω and T. If ω = 8.2*102 rad/s, calculate T in seconds. (Remember, that a radian equals one.) T might be a fraction of a second.The quantities A and p (called the amplitude and the phase) are undetermined by the differential equation. They are determined by initial conditions -- specifically, the initial position and the initial velocity -- usually at t = 0, but sometimes at another time. In the oscillating part of the experiment, I measured only the time of 30 periods. I measured no position or velocity. Consequently, A and p (and also yo) are irrelevant in the problem. We only compare the period T or the frequency w with the theoretical prediction. You have (hopefully) derived (or maybe looked up) the relation between w and k and m. This final question relates w and T. If w = 5.8*10° rad/s, calculate T in seconds. (Remember, that a radian equals one.) T might be a fraction of a second.
- A spring with a spring constant of 200 N/m with a 5 kg mass attached to it has the following position function. ?(?) = 5 cos (0.3 ?) (The 5 has units of m and the time is in seconds.) What is the frequency of oscillation for the mass? What is the period of oscillation?(a) An oscillating object repeats its motion every 3.3 seconds. (i) What is the period of this oscillation? (ii) What is its frequency? (iii) What is its phase rate (i.e. angular frequency)? (b) A magnesium atom (mass of 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 10l3 Hz. What is the effective spring constant of the forces holding that atom in the crystal? (c) Sitting on a trampoline, a person with mass m sinks a distance Az below the trampoline's normal level surface. (i) If the person gently bounces on the trampoline (without leaving its surface), what would be the person's period of oscillation T? (You should not need the person's mass, but if you think you do, assume and state a value.) (ii) Find T for Az = 45 cm. Check: For Az = 20 cm you should find T = 0.90 s.