Amass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. the record of time is started when the oscillating mass first passes through the equilibrium position, and the position of the mass at any time is described by x = (3.9 cm)sin[(9.3 rad/s)πt]. determine the following.

(a) frequency of the motion hz.
(b) period of the motion.
(c) amplitude of the motion cm.
(d) first time after t = 0 that the object reaches the position x = 2.6 cm

Answer

given,

x = (3.9 cm)sin[(9.3 rad/s)πt]

general equation of displacement

x = A sin ω t

A is amplitude

now on comparing

c) Amplitude  =3.9 cm

a) frequency =

           f = 4.65 Hz

b) period of motion

        T = 0.215 s

d) time when displacement is equal to x= 2.6 cm

x = (3.9 cm)sin[(9.3 rad/s)πt]

2.6 = (3.9 cm)sin[(9.3 rad/s)πt]

sin[(9.3 rad/s)πt] = 0.667

9.3 π t = 0.73

t = 0.025 s

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

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