Please help simple harmonic motion problem?

Question

a weight is attached to a suspended spring is set into a vertical simple harmonic motion. The motion can be described as d=2sin(4πt) with d in cm and t in sec.

Determine:

a)the start position of the weight at t=0.0 sec

b)the amplitude of the motion A

c) the angular velocity, ω

d)the periodic time, T.

e) the frequency,f

f) the location of the weight at t=2.25 sec

this is what i got so far

a)?

b) 2cm

c)ω=4π

d)1/2π

e)2π

f)?

please check my work and pleeeeeaaaaaase show me how to get a and f

thanks

Answer 1

both (a) and (f) merely require substitution into the equation of motion you are given:

(a)

at t=0, d = 2sin(0) = 0

(fyi: this is not terribly realistic, as you would more likely stretch the spring at let go at t=0)

(f)

at t=2.25, d = 2 sin ( 28.274 ) = (2)(0.474)= 0.947 cm

(d) and (e) are incorrect:

omega=2 pi f    and     T = 1/f

therefore, f = 4 pi / 2 pi = 2 Hz

T = 0.5 seconds