Ablock with a mass of 0.600 kg is connected to a spring, displaced in the positive direction a distance of 50.0 cm from equilibrium, and released from rest at t = 0. the block then oscillates without friction on a horizontal surface. after being released, the first time the block is a distance of 35.0 cm from equilibrium is at t = 0.200 s.(a) what is the block's period of oscillation? (b) what is the the value of the spring constant? (c) what is the block's velocity at t = 0.200 s? (indicate the direction with the sign of your answer.(d) what is the block's acceleration at t = 0.200 s? (indicate the direction with the sign of your answer.

Explanation:

The amplitude of the oscillation under SHM will be .5 m and the equation of

SHM can be written as follows

x = .5 sin(ωt + π/2) , here the initial phase is π/2 because when t = 0 , x = A ( amplitude) , ω is angular frequency.

x = .5 cosωt

given , when t = .2 s , x = .35 m

.35 = .5 cos ωt

ωt = .79

ω = .79 / .20

= 3.95 rad /s

period of oscillation

T = 2π / ω

= 2 x 3.14 / 3.95

= 1.6 s

b )

ω =

ω² = k / m

k = ω² x m

= 3.95² x .6

= 9.36 N/s

c )

v = ω

At t = .2 , x = .35

v = 3.95

= 3.95 x .357

= 1.41 m/ s

d )

Acceleration at x

a = ω² x

= 3.95 x .35

= 1.3825 m s⁻²

50 inches should be the resultant vector

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.