Problem 2d The graph shows the position of a harmonic oscillator with mass m 0.700 kg on the x-axis. What is the phase constant of this oscillator? Assume the form r Acos(wt + 0 t (s) This problem does not use rounded numbers. Use the graph to derive the most accurate numbers possible. Marking will take into account the fact that you cannot read the graph with infinite precision. Show your work!
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- A mass of 1 slug is attached to a spring whose constant is 25 / 4 lb / ft. Initially the mass is released 1 ft above the equilibrium position with a downward velocity of 3 ft / sec, and the subsequent motion takes place in a medium that offers a damping force numerically equal to 3 times the instantaneous velocity. An external force ƒ(t) is driving the system, but assume that initially ƒ(t) K 0. Formulate and solve an initial value problem that models the given system. Interpret your results.Solve for the frequency of a vibrating pendulum if it has a length of 2 m. What will be its period? If you disregard the length provided (2m), what will be the length of the pendulum if period (T) is given with a value of 3 seconds? Show your formula transformation.In Problem ,the distance d(in meters) of the bob of a pendulum of mass m(in kilograms) from its rest position at time t(in seconds) is given.The bob is released from the left of its rest position and represents a negative direction. (a) Describe the motion of the object.Be sure to give the mass and damping factor. (b) What is the initial displacement of the bob? That is,what is the displacement at t = 0? (c) Graph the motion using a graphing utility. (d) What is the displacement of the bob at the start of the second oscillation? (e) What happens to the displacement of the bob as time increases without bound?
- The two graphs as shown are for two different vertical mass-spring systems.a. What is the frequency of system A? What is the first time at which the masshas maximum speed while traveling in the upward direction?b. What is the period of system B? What is the first time at which the mechanical energy is all potential?c. If both systems have the same mass, what is the ratio kA/kB of their spring constants?A block of mass m = 2 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is initially at the equilibrium point at x = 0 m where the spring is at its natural length. Then theblock is set into a simple harmonic oscillation with an initial velocity 2.5 m/s at x = 0 cm towards right. Thehorizontal surface is frictionless. a) What is the period of block’s oscillation? b) Find the amplitude A of the oscillation, which is the farthest length spring is stretched to. c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motion graphx(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motion graph.Assume the clock starts from when the block is just released. d) Please find out the block’s acceleration when it is at position x = 5cm. e) On the motion graph you draw for part c), please mark with diamonds ♦ where the kinetic energy of theblock is totally transferred to the spring…Christine Karera hangs a spring and it oscillates at a frequency of 60 cycles in a minute when an object is attached to it. A. Calculate the mass of the object if the spring constant is 250 N/m. Show your formula transformation. B. Solve for the frequency of a vibrating pendulum if it has a length of 2 m. What will be its period? If you disregard the length provided (2m), what will be the length of the pendulum if period (T) is given with a value of 3 seconds? Show your formula transformation.
- A mass m is connected to the bottom of a vertical spring whose force constant is k. Attached to the bottom of the mass is a string that is connected to a second mass m , as shown in the figure(Figure 1). Both masses are undergoing simple harmonic vertical motion of amplitude A. At the instant when the acceleration of the masses is a maximum in the upward direction the string breaks, allowing the lower mass to drop to the floor. Find the resulting amplitude of motion of the remaining mass. (Express your answer in terms of the variables A, m, k, and appropriate constants)Please provide solutions please to the following problem. Thank you. Consider the system below; the pendulum (with mass m and length L) is connected to a freely moving block (with mass m). Assume that the surface where the block slides horizontally has negligible friction and the block is connected to a wall by a spring with spring constant k. Determine the (a) frequencies of the normal modes for small oscillations around the equilibrium positions and (b) the motion for each of the normal modes for special case where ??= √??=√??. Use Lagrangian formulations to solve the problem. RaphaelSolve the problem. PROVIDE THE GIVEN, REQUIRED, EQUATION, SOLUTION, AND FINAL ANSWER Many single-celled organisms propel themselves through water with long tails, which they wiggle back and forth. (The most obvious example is the sperm cell.) The frequency of the tail’s vibration is typically about 10-15 Hz. To what range of periods does this range of frequencies correspond?
- The phase space trajectory of an undamped oscillator is shown below. In the diagram, eachdivision along the position axis corresponds to 0.1 m; along the velocity axis, 0.10 m/s. What is the angular frequency ?Aof the undamped oscillator? Explain how you can tell.Below is the depicted graph of the velocity of a block that is connected to a spring with an unspecified mass and a force constant of 80 N/m, undergoing oscillation. The time axis is wrongly marked for 1.6 sec. It should be 1.8 sec. Determine the period, frequency, and angular frequency of oscillation? Calculate the maximum displacement of the mass from equilibrium in centimeters? Just so you know: It does not correspond to the amplitude of the velocity graph. What is the peak acceleration of the mass and identify the moments when it transpires?A block of mass m = 1 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is pulled to a position x = 10 cm to the right of equilibrium and released from rest. The horizontalsurface is frictionless.(a) What’s the period of block’s oscillation? (b) Find the speed of the block as it passes through the equilibrium point x = 0. (c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motiongraph x(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motiongraph. Assume the clock starts from when the block is just released. (d) Please find out the block’s velocity and acceleration at t = 0.14s.