3 b) A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Find the time (in s) at which the mass attains its extreme displacement from the equilibrium position (the extreme distance after passing the equilibrium position.) Round your answer to two digits after the decimal sign.
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- The spring is 5 cm at its natural length. When at equilibrium (e.g. see figure) its length becomes 50 cm. The cart’s mass is 273 gr and the hanging weight is 300 gr. The cart and weight are set into oscillation. Derive the theoretical period as a function of the two masses and the spring constant (no air resistance or friction). Show methodology and discrete steps.A box of mass 0.850 kg is attached to a spring with k = 145 N/m and set into simple harmonic motion on a frictionless, horizontal table. The amplitude of motion is 5.10 cm. (Use the exact values you enter in previous answer(s) to make later calculation(s).) (a) What is the total energy of the box–spring system? ______ J (b) What is the speed of the box when the spring is compressed by 2.00 cm? (Give your answer to at least two decimal places.) ______m/s (c) What is the kinetic energy of the box at this position? ______ J (d) What is the potential energy of the box–spring system at this position? ______ JA 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…
- A meter stick is attached to one end of a rigid rod with negligible mass of length / = 0.787 m. The other end of the light rod is suspended from a pivot point, as shown in the figure below. The entire system is pulled to a small angle and released from rest. It then begins to oscillate. (a) What is the period of oscillation of the system (in s)? (Round your answer to at least three decimal places.) 1 2.340 S (b) By what percentage does the period of the system found in part (a) differ from the period of a simple pendulum 1.287 m long? IT simple - Tsystem! 2 x 100% = simple How is the period of a simple pendulum related to length? Use the period of a simple pendulum and the period found in part (a) in the given formula. %A grandfather clock has a pendulum that consists of a thin brass disk of radius r and mass m that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in the figure below. If the pendulum is to have a period I for small oscillations, what must be the rod length L? (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.) L = Rotation axis LFor a simple harmonic oscillator with x = A sin ot write down an expression for the velocity. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For trigonometric functions use the usual sin and cos, while for Greek letters such as w, use omega. Please use the "Display response" button to check you entered the answer you expect. U= Display response
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- 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.A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 3 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = Find the time at which the mass attains its extreme displacement from the equilibrium position. t= X x What is the position of the mass at this instant? The extreme displacement is x = 0.39 X feet.A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. Find the following part a and b. A) Find the equation of motion, x(t). B) What type of damped motion is this system?