
3) If the period of a mass spring system is 1.5s, and the spring constant is...
(a) Find the period of oscillation for a spring-mass system where the spring constant (k) is 24 N/m and the mass (m) is 6 kg. (b) Write an equation for x(t) if the spring is stretched to an amplitude of 10 cm from its equilibrium position x = 0 at t = 0. (c) Write an equation for the following initial conditions: at t = 0, the mass is at x = 0 and has a velocity of +3 cm/s.
An ideal horizontal spring-mass system oscillates with a period of 0.60 seconds. The mass is 3 kg but the spring constant is not known. When this same spring and mass are arranged to hang vertically, the frequency of oscillations will be: a) 0.40 Hz b) 1.2 Hz c) 2.5 Hz d) none of the above are correct e) the spring constant is needed to determine the frequency
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
What is the period of the oscillations of a mass-spring system, measured in seconds, if the mass of the object is 4.4kg and the spring constant (or force constant) is 27.7N/m?
A 5.95 kg mass oscillates up and down on a spring that has a force constant of 90 N/m. (a) What is the angular frequency of this spring/mass system? (b) What is the period of this spring/mass 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) .
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
A mass m = 3 kg is attached to a spring with spring constant k = 3 N/m and oscillates with simple harmonic motion along the x-axis with an amplitude A = 0.10 m. (a) What is the angular frequency of this oscillation? (b) What is the period T and the frequency f of the oscillation? (c) If the phase constant = 0, write down expressions for the displacement, velocity and acceleration of the mass as a function...
The period of oscillation for a mass-on-a-spring system is 0.20 s. If m = 4.0 kg, what is the spring constant of the spring? N/m
Consider a vertical mass-spring system. The spring constant is k = 48N the mass is m = 1.0 kg. (a) Find the angular frequency. The mass is pulled from equilibrium 0.10 m down. (b) Write the equation for the displacement as a function of time, with a vertical xaxis pointing upward.