Simple harmonic motion

Question

When a mass spring system is stretched 3cm from its equilibrium position it starts to preform simple harmonic motion with a frequency of 10Hz at what instant does it first pass the following positions?

A)x1=1.5cm

B)x2=-3cm 

Answer 1

x(t) = A cos(ωt + φ) 

 

A = 3 cm

 

x(t) = 3cos(ωt + φ)

 

x(0) = 3 ⇒ φ = 0

 

ω = 2πf = 2π(10) rad/s = 20π rad/s

 

x(t) = 3 cos(20πt)

 

(A)

 

1.5 = 3 cos(20πt)  [The argument is in radians.]

 

0.5 = cos(20πt) ⇒

 

20πt = π/3 ⇒

 

t = 1/60 sec

 

(B)

 

-3 = 3cos(20πt)  [The argument is in radians.]

 

cos(20πt) = -1 ⇒

 

20πt = π ⇒

 

t = 1/20 sec

 

Test both answers.  You will see that they work.