A body of mass 25g is under simple hormonic motion theforce constant is k= 400 d

Question

A body of mass 25g is under simple hormonic motion theforce constant is k= 400 dyn/cm the motion is started by displacingthe position of body 10 cm from the mean (right side to the bodyequlibrium position)   by imparting the velocity of of 40 cm/sec compute a) maximium displacement (A) b)time period c)angular velocity d)frequency e)total energy f)maximium velocity g)initial phase 0 h)the new equatios of motion when t=/8 sec A body of mass 25g is under simple hormonic motion theforce constant is k= 400 dyn/cm the motion is started by displacingthe position of body 10 cm from the mean (right side to the bodyequlibrium position)   by imparting the velocity of of 40 cm/sec compute a) maximium displacement (A) b)time period c)angular velocity d)frequency e)total energy f)maximium velocity g)initial phase 0 h)the new equatios of motion when t=/8 sec h)the new equatios of motion when t=/8 sec

Explanation / Answer

m = 25 g, k = 400 dyn/cm, x0 = 10 cm, v0= 40 cm/sec = (k/m) = 4.0 rad/s
compute a) maximium displacement (A)
A = [x02 + (v/)2] =141 cm

b)time period
T = 2/ = 1.57 s

c) angular velocity
= 4.0 rad/s

d)frequency
f = 1/T = 0.637 Hz

e)total energy
kA2/2 = 4.00*104 erg

f)maximium velocity
vmax = A = 564 cm/s

g)initial phase 0
tan-1[-v0/(x0)]= -/4

h)the new equatios of motion when t=/8 sec
x = 141 cos(4*/8 - /4) = 141 cos(/4) = 100 cm

h)the new equatios of motion when t=/8 sec
x = 141 cos(4*/8 - /4) = 141 cos(/4) = 100 cm

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