This Question 1 pt A weight on a vertical spring is given an

This Question: 1 pt A weight on a vertical spring is given an initial upward velocity of 4 cm/sec from a point 2 centimeters above eq location 5 seconds after it is set in motion Write the formula for the weight\'s location. Type an expression using t as the variable.) After 5 seconds, the location of the weight, x, is cm. Round to the nearest tenth as needed.)

Solution

Equation for motion of a spring is given by :

x = (v₀)/k sin(kt) + x₀ cos(kt)

In this case, v₀ = -4cm/sec (negative sign shows upward displacement)

and x₀ = 2

We have k = 1

So we get :

x = -4sin(t) + 2cos(t)

For t=5sec

x = -4sin(5) + 2cos(5)

=>x = -4(0.087156) + 2(0.99619)

=> x = -0.348624+1.99238

=> x = 1.6 cm