Suppose a spring mass system has a mass of 2.0 kg and the amplitude has a half-life of 0.4 seconds. What is the damping constant of the system?
Suppose a spring mass system has a mass of 2.0 kg and the amplitude has a...
A mass of 1.32 kg is connected to a spring of spring constant 8.81 N/m . An oscillation is started by pulling the mass to the right to amplitude 0.582m before release and the oscillator moves in air. The oscillation decays to 18.2% of the original amplitude in 58.2 seconds. the damping constant of the oscillation is 7.73*10^-2 kg/s total energy has the system lost in this time due to air damping = 1.44 j the amplitude of the oscillation...
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg. Its free response amplitude decays such that the amplitude of the 30th cycle is 20% of the amplitude of the 1st cycle. It takes 60 sec to complete 30 cycles. Estimate the damping constant c and the spring constant k.
A 2.0 kg mass sits on top of a vertical spring that has a spring constant k=100 N/m. A second 2.0 kg mass is dropped from rest starting 1.0 m above the first mass. The dropped mass sticks to the first mass (Velcro) and the masses begin to bounce up and down on the spring. What is the period of the oscillation? What is the amplitude of the oscillation? How much time elapses between the time the masses collide and...
A mass-spring system rests on a rough table. Its initial amplitude is 20 cm. The spring constant is 20 N/m and the mass is 2.0 kg. If 0.30 J of energy is lost to friction during the first oscillation, what is the amplitude at the beginning of the second oscillation?
Suppose a mass of 2.0 kg hangs in an elevator from a spring of unknown spring constant, k. Before the elevator moves the mass is 1.0 m from the ceiling. While the elevator is accelerating upwards at 1.0 m/s2 , the spring stretches an additional 5.0 cm. What is the spring constant k?
A damped harmonic oscillator consists of a block of mass 3 kg and a spring with spring constant k=7 N/m. Initially, the system oscillates with an amplitude of 23 cm. Because of the damping, the amplitude loses 60% of its initial value by the end of four oscillations. a.) What is the value of the damping constant, b? b =? b.) What percentage of initial energy has been lost during these four oscillations? %=?
A horizontal spring mass system is to be constructed. A spring which has a spring constant of 3 kg/s2 will be used. The system should be designed so that when it is released and vibrating freely (there is no forcing) the amplitude of its vibrations will decay like ?−0.4t, and it should oscillate with a period of 4 seconds. (Although the motion is oscillatory it is not strictly periodic because the amplitude decays exponentially. In this context "period" refers to...
Differntial Equations Forced Spring Motion
1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force F(t) = ( 12.0N) cos(ϝt) is applied to the mass, and the damping coefficient b is 6.00 Ns/m. What is the amplitude (in cm) of the steady-state motion if ϝ is equal to half of the natural frequency ϝ0 of the system?
3. A spring-mass system has mass m, spring constant k, and hence natural frequency ω0 = (k/m)^1/2 . The damping constant can take any value. Show that the smallest half-life you can get without the spring becoming overdamped is (ln2 / ω0) .