Question

A mass of 50 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 50 cms, and if there is no damping, determine the position u of the mass at any time t. Enclose arguments of functions in parentheses. For example, sin(2x). Assume g=9.8 ms2. Enter an exact answer. u(t)= m When does the mass first return to its equilibrium position? Enter an exact answer. t=

Answer 1

mass is m=50 gram

spring stretches x=1.568 cm

spring constant is given by

there is no damping so c=0

.

DE is given by

find roots

.

for complex roots, the general solution is

....................(1)

the mass is set in motion from its equilibrium position so y(0)=0

..................put it back in equation 1

.

....................(2)

take derivative

initial downward velocity is 50 cms so y'(0)=50

..................put it back in equation 2

.

.

take y=0 for equilibrium position

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