A mass-spring system of mass m 1 kg and spring constant k = 100 N/m is set into vibration with an amplitude A = 20 cm. If the acceleration at a given position x is a = - 8 m/s^2, then the velocity at the same position is: %3D
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- The position with time of an object is given by x(t)=Acos(ωt)If the amplitude is 1.52 m, and the frequency is 1.4 Hz, what is the object's velocity at 16.25 seconds?A mass of 8.0 kg hangs from a spring attached to the ceiling. The spring has a spring constant of 500 N/m and it stretches 15.7 cm from its mean position. A student grabs the spring, applies a force and stretches it a further 6.7 cm downwards. The block is released and initially accelerates upward before undergoing simple harmonic motion. Calculate the initial vertical acceleration of the mass. (Units: m/s? , to 2 sig figs)The displacement of a swinging ball in simple harmonic motion is modeled by the equation d=3sin(21t), where t is measured in seconds. If d is measured in centimeters, what is the displacement to the nearest centimeter when t=14? NOTE: The angle is in radians.
- The position of an object in harmonic motion on the end of a spring is p= 2 cos(3t)- 4sin(3t),where is measured in seconds and is measured in inches. What is the velocity (in in/s) of the object at t= pi/3 seconds?Some passengers on an ocean cruise may suffer from motion sickness as the ship rocks back and forth on the waves. At one position on the ship, passengers experience a vertical motion of amplitude 1.5 m with a period of 13 s. Part A: What is the maximum acceleration of the passengers during this motion? Express your answer using one significant figure. Part B: What fraction is this of g ? Express your answer using one significant figure.A mass of 6.33 kg is placed on a vertical spring. What is the spring constant, in N/m, of a mass-spring system with a period of 0.6 s?
- A 1.4 kg mass attached to a horizontal spring oscillates at a frequency of 2.1 Hz. At t =0 s, the mass is at x= 1.1 m and has vx =− 2.9 m/s. What is the position (in meters) at t =2 s?What is the maximum velocity (in m/s) of a 51.0 kg person bouncing on a bathroom scale having a force constant of 1.35 ✕ 105 N/m if the amplitude of the bounce is 0.200 cm?A 50 cm long spring with spring constant 257 N/m has a mass 1.9 kg attached to it, and it can oscillate on a horizontal table without any friction. When the spring is pulled so that its length is 55 cm, what is the magnitude of the maximum acceleration of the mass? Give your answer in m/s?.
- 券 A child bounces in a harness suspended from a door frame by three elastic bands. (a) If each elastic band stretches 0.200 m while supporting a 5.95-kg child, what is the force constant for each elastic band? N/m (b) What is the time for one complete bounce of this child? (c) What is the child's maximum velocity if the amplitude of her bounce is 0.200 m? m/sThe human eardrum responds to sound by vibrating. If the eardrum moves in simple harmonic motion at a frequency of 4.22 kHz and an amplitude of 0.110 nm (roughly the diameter of a single hydrogen atom), what is its maximum speed of vibration? (Amazingly, the ear can detect vibrations with amplitudes even smaller than this!) μm/sHrlp