Zontini the Amazing Hypnotist is hypnotizing a volunteer at a performance by swinging a pocket watch back and forth in front of her face. The pocket watch's
current distance from center in centimetres in terms of time is modelled by the
equation d(s) = 7 sin(360s). If Zontini the Amazing Hypnotist were to swing the watch
twice as fast, covering the same distance, how would the equation change?

The equation will change by an increase in the angular frequency of motion by a factor of 2 to become  d(s) = 7·sin(720s)

Step-by-step explanation:

The given oscillatory motion equation of the swinging pocket watch is d(s) = 7sin(360s)

The general equation of simple harmonic motion is x = A·sin(ω₁t + ∅)

Comparing, we have;

x = d(s)

A = 7

ω₁t = 360

∅ = 0

The period of oscillation = The time to complete a cycle =  2·π/ω₁

Therefore;

ω₁ = 2·π/T₁

When the cycle or the watch swing rate is doubled, the time taken to compete one cycle is halved and the new period, T₂ = T₁/2

ω₂ = 2·π/T₂  = 2·π/(T₁/2) = 4·π/T₁ = 2ω₁

The equation becomes;

x = A·sin(ω₂t) =  A·sin(2ω₁t) which gives;

d(s) = 7·sin(2 × 360s) = 7·sin(720s)

The equation will change by the doubling of the angular frequency of the motion

idk

step-by-step explanation: