Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x = (6.4 cm)cos[2nt/(1.58 s)]. Determine the following. (a) period of the motion 1.58 S (b) frequency of the oscillations 0.633 Hz (c) first time the mass is at the position x = 0 S (d) first time the mass is at the site of maximum compression of the spring S

Answer 1

given equation

x = (6.4 cm)cos[2πt/1.58s ]

compare to the

x =A cos[ 2πt /T]

then we get

a)

we get time period is T = 1.58 s

b)

frequency f = 1/T

f = (1/1.58 ) Hz

f = 0.633 Hz

c)

plugging the value x=0

x = (6.4 cm)cos[2πt/1.58s ]

then

0 = (6.4 cm)cos[2πt/1.58s ]

cos^-1(0) = 2πt/1.58s

π/2 =  2πt/1.58s

t = 1.58/4 = 0.395 s

t =0.395 s

d)

given condition is x=A

SO

x =A cos[ 2πt /T]

A =A cos[ 2πt /T]

1 = cos[ 2πt /T]

cos^-1(1) = 2πt/1.58s)

π=2πt /1.58

t = 1.58 / 2 = 0.79s

t = 0.79 s

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