Question

The position of a mass oscillating on a spring is given by x = ( 3.6 cm)cos[2pi t/(0.67s)].
A. What is the period of this motion?
T=? s
B. What is the first time the mass is at the position x = 0?
t=? s

Answer 1

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The position of a mass oscillating on a spring is given byx= (6.8cm)cos[2πt/(0.91s)].

(a) What is the frequency of this motion?
(b) When is the mass first at the positionx=-6.8cm?

ANSWER:

givenThe position of a mass oscillating on a spring isx= (6.8cm) cos[2πt/(0.91s)]--------(1)a)we knowx = Acos[2πt/T] -------(2)whereT = time periodand frequency f = 1/Tcomparing (1) &(2) we getf = 1 / 0.91s= 1.1Hzb)from the figure it is clear that the time taken (t) to be atthe position x = -6.8cm for the first time is equal to thetime taken between 6.8cm to -6.8cm that is T/2so, t = T/2=0.91s /2=0.455 s