The displacement of a SHM in a string is a cosine function of time X = 3.5 Cos 2

ID: 1571486 • Letter: T

Question

The displacement of a SHM in a string is a cosine function of time

X = 3.5 Cos 25.0 t

3.5 is in meters.

The formula you need for this problem.

X = A Cos( t)

V m = A

a m = A 2

= 2 f = 2 /T

You need to show all the formulas, calculations, and unit to receive the whole credit.

Find the following. You must write the symbol, and also unit for each quantity.

Amplitude of the string particles

b)) angular frequency,

Frequency,

Period

Displacement at t= 2 seconds,

Maximum velocity of the string particles,

g) Maximum acceleration of the string particles.

Amplitude of the string particles, A = 3.5 m

(b) Angular frequency, w = 25 rad/s.

Frequency, f = w / (2*pi) = 25 / (2*3.141) = .3.98 Hz

Period, T = 1/f = 1 / 3.98 = 0.251 s

Displacement at t = 2 s

X = 3.5*cos (25*2) = 3.38 m

Maximum velocity, Vm = A*w = 3.5*25 = 87.5 m/s.

(g) Maximum accleration = A*w^2 = 3.5*25^2 = 2187.5 m/s^2

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