The equation of motion for a simple harmonic oscillator (SHO) is:
m(d2x/ dt2) = −kx
where m is the mass and k the spring constant. A generic solution of the above differential equation can be written in the form:
x(t) = A cos(ωt + φ0).
Where ω = p k/m and A and φ0 are arbitrary constants to be determined by the initial conditions of the motion. You are given the following information: a block of mass m = 10 kg is attached to a spring with spring constant k = 2.5N/m; at time t = 0 the amplitude of the motion is 0, and the velocity is -5 m/s.
(a) Using the generic solution (1) above find the form x(t) for the position as a function of time for the block (you need to determine the constants A, ω and φ0). Do not forget to write clearly the appropriate dimension for each quantity, A, φ0, ω.
(b) Plot the function x(t) that you found in part (a) from t = 0 until t = 20s.
(You can use a graphical calculator or WolframAlpha or Desmos to make your plot)