A horizontal spring is lying on a frictionless surface. One end of the spring is attaches to a wall while the other end is connected to a movable object. The spring and object are compressed by 0.080 m, released from rest, and subsequently oscillate back and forth with an angular frequency of 12.1 rad/s. What is the speed of the object at the instant when the spring is stretched by 0.041 m relative to its unstrained length

-0.831 m/s

Explanation:

With amplitude A = 0.08 m and angular frequency ω = 12.1 rad/s, we have the following simple harmonic equations of motion:

Distance: x(t) = Acos(ωt) = 0.08cos(12.1t)

Speed: v(t) = -Aωsin(ωt) = -0.08*12.1sin(12.1t) = -0.968sin(12.1t)

At distance = 0.041, we can solve for 12.1t

x(t) = 0.041

0.08cos(12.1t) = 0.041

cos(12.1t) = 0.5125

12.1t = 1.033

t = 0.085s

Use it to plug into the v(t) equation

v(0.085) = -0.968sin(12.1*0.085) = -0.968*sin(1.033) = -0.968*0.859 = -0.831 m/s

mass and volume are the answers you are looking for

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.