Question

direction, has vel()city given by: simple harmonic oscillator, with ()scillations in the . rad (a) Find the values of w, A, f, T, and φ (b) Find r(11), u(11), and a(11) for ti = 0.5s

Answer 1

(a) Compare the given equation with v = yax sin (ot) Angular frequency of the vibrating particle is o 6.9 rad/s Time period of the vibrating particle is 6.9rad's T" 6.9rad/s 0.9s Frequency of the vibrating particle is, T" 1.1Hz Maximum speed of the parti cle is, A 2.2m/s Amplitude of vibrating particle is 2.2m/s 6.9rad/s 0.32m (b)Velocity of the parti cle is the rate of change of position. (2.2m/s)sn((6.9rad/s)) x=「(2.2m/s)sin((6.9rad/s)t) 2.2m/s 6.9rad/s cos (6.9rad/s )t -0.32 cos[(6.9rad/s)t -00.32 cos (6.9rad/s) (0.5s )] s 0.305m У,-0,-(2.2m/s)sin ((6.9rad's) (0.5s 0.67m Acceleration of the particle is the rate of change of velocity dt =dt((22m/s)sin((69rad's))) [(2.2m/s) (6.9rad/s)cos(6.9rad/s)) a,-Jsx-15.18cos(6.9rad/s) (0.5s) --14.5m/s