a simple harmonic motion is represented by x=4sin[3t+3.14/4].find the angular frequency and amplitude and what is the velocity and acceleration at t=1 second.
sin(kt) has period 2π/k. So, its frequency is k/2π. But ω=2πf = k
so, ω=3
amplitude is clearly 4, since sin(t) has amplitude 1
for v and a, just take derivatives:
x = 4sin(3t+π/4)
x' = 12cos(3t+π/4)
x" = -36sin(3t+π/4)
now just plug in t=1