A spring with a stiffness of 300 N/m is connected to a 15 kg mass. A displacement of 60 cm to the right of the equilibrium position is applied to the mass initially. It began oscillating against a frictionless surface after being released from rest. Find the position, velocity and acceleration at t = 4s.

A spring with a stiffness of 300 N/m is connected to a 15 kg mass. A displacement of 60 cm to the right of the equilibrium position is applied to the mass initially. It began oscillating against a frictionless surface after being released from rest. Find the position, velocity and acceleration at t = 4s.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.13P

See similar textbooks

Similar questions

A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.
A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a more pliable material.
An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, what is the period of the motion? (a) 2T (b) 2T (c) T (d) T/2 (e) T/2
Consider an undamped linear oscillator with a natural frequency ω0 = 0.5 rad/s and the step function a = 1 m/s2. Calculate and sketch the response function for an impulse forcing function acting for a time τ = 2π/ω0. Give a physical interpretation of the results.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
If the speed of the observer is increased by 5.0%, what is the period of the pendulum when measured by this observer?
Obtain the response of a linear oscillator to a step function and to an impulse function (in the limit τ → 0) for overdamping. Sketch the response functions.
A spring with a stiffness of 300 N/m is connected to a 15 kg mass. A displacement of 60 cm to the right of the equilibrium position is applied to the mass initially. It began oscillating against a frictionless surface after being released from rest. What is the maximum velocity and acceleration of mass ?
For a 15 kg mass, a 300 N/m stiffness spring is used. An initial 60-centimeter displacement is applied to the mass, starting from equilibrium. As soon as it was let go, it began oscillating against a smooth surface. What is the maximum velocity and acceleration of mass ?
In this experiment, you have a spring of spring constant 62N/m. When a small mass is oscillating on the spring, measurement data shows that the amplitude of the oscillation is 4.27cm; while the highest speed of the mass is 4.04m/s. What is the mass of the object (in unit of gram)?
A spring (200 N/m) is attached to a mass (0.4kg) and are positioned horizontally. When the mass is at x = 2 cm it is the mass moving at 1.3 m/s. Write an equation for the position of the mass with respect to time. Assume that at t = 0 the mass is passing through equilibrium.