Question

2. The harmonic oscillator in the figure has a position function x(t) A cos(at + φ), where A = 6 cm, what is the phase constant φ? A) 70.5o or 70.5° B) 109.5° or 199.5° C) 109.5° D) 199.5° E) none of the above x (cm)

answer is C why ?

Answer 1

From the figure it is clear that at t = 0 sec , x = -2 cm

So put these values in the given equation we have

- 2cm = 6cm cos ( w x 0 + phi )

or cos (phi) = -1/3 ==> phi = cos^-1 (-1/3) = 109.5 ^o

Answer 2

ANSWER :

Given :  x(t) = A (ωt + ϕ)

From the given figure : 

A = 3 cm.

At t = 0, x(0) = 3 cos (ϕ) 

=> - 1 = 3 cos(ϕ) 

=> ϕ = cos ^(-1) (- 1/3)

=> ϕ = 1.9106 rad. = 109.5267 º or 199.5267 º

So, ANSWER is Option C : 109.5 º or 199.5 º 

Answer 3

ANSWER :

Given :  x(t) = A (ωt + ϕ)

From the given figure : 

A = 6 cm.

At t = 0, x(0) = 6 cos (ϕ) 

=> - 2 = 6 cos(ϕ) 

=> cos (phi) = - 2/6 = - 1/3 

=> ϕ = cos ^(-1) (- 1/3)

=> ϕ = 1.9106 rad. = 109.5267 º or 199.5267 º

So, ANSWER is Option C : 109.5 º or 199.5 º