Single Degree-of-Freedom Systems

[aminbpy]

An SDOF system (m = 20 kg, k = 350 N/m) is given an initial displacement of
10 mm and initial velocity of 100 mm/s. (a) Find the natural frequency; (b) the
period of vibration; (c) the amplitude of vibration; and (d) the time at which the
third maximum peak occurs.
Ans: 0.666 Hz; 1.502 sec; 25.91 mm; 3.285 sec.



Which Equation should I use to obtain the amplitude of vibration and time for the third maximum pick occur?


Part a and b I got the answer.

 

[hilbert2]

That's a harmonic oscillator, isn't it? Calculate the total energy (kinetic plus potential) at the initial moment from the equation $E=\frac{1}{2}mv^{2}+\frac{1}{2}kx^{2}$, and find out what displacement $x$ it corresponds to if all the energy were potential energy. That way you can find the amplitude of oscillation.