An oscillating spring-mass system has a mechanical energy of 2.5 J. If the position amplitude is 0.02 m, and the acceleration amplitude is 5 m/s2, find (a) the spring constant and the mass of the block. If the position of the mass at t=0 is x=0.02 m, and at t=T/4 is x=0, express the position as a function of time

Please help me

A mass-spring motion is governed by the ordinary differential equation d²x dx +b + k(t)x= F(t), dt² dt m where m is the mass, b is the damping constant, k is the spring constant, and F(t) is the external force. We consider the initial conditions x(0) = 1 and x/(0) = 0. Assume the following numerical values for this part of the project: m = 1, k = 1/5, b= 1/5, and F(t) = cos yt. 1 (a) Read section 4.10. Explain what is the resonance frequency, and then compute the resonance frequency for this mass-spring system. (b) The ODE45-solver can be used to obtain the solution curves in MATLAB. Use the script Project2_Q2.m to plot the solutions and estimate the amplitude A of the steady response for y = 0.2, 0.42, 0.6, and 0.8. (c) The script also provide you with the graph of A versus y. For what frequency 7 is the amplitude the greatest? Is it equal to that you obtained in (a)?

A simple pendulum has a length of 52.6 cm and makes 81.8 complete oscillations in 2.00 min. (a) Find the period of the pendulum. IS (b) Find the value of g at the location of the pendulum. .2 m/s?