Question

The motion of an object moving in simple harmonic motion is given by x(t) = (0.1 m) [cos (ot) + sin (ot)] where o = 31. (a) Determine the velocity and acceleration equations. (b) Determine the position, velocity, and acceleration at time t = 2.4 s.

Answer 1

Given, w=3T position, alt) = (ool m) [con (wt) + sin (wto] = oil [ con att & sin ant] a) velocity, ult) = dact) at = [on(con att & sin 37+)] = 0.1 [- 3TT sin 3TT + + 3T CO 3T1] = 0.942 C-sin 31t & conant) Acceleration, act) = ducto at # [ 0.942 C-sin 37T ++ Cops 3T )] = 0.942 [- 3T chatt - 34 sín 31+ = -8,878 Cenantt sin 3 tt) when t=2.4s X(t) = 0.1 [co (3TX274) + sin (3 T%2:40] = -0.140 rect) = 0.942[- sin (31x214)+con (3TX 2.4] = -0. 208 m/s alt) = -8.878 [co (3T *2.4) + sin (31x2:47] - 12.40! m/s2