A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measured in seconds and s is in inches: s(t)=−3cos(πt+π4). Determine the position of the spring at t=1.5 s. Find the velocity of the spring at t=1.5 s.

The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

Explanation:

Given that,

The position function,

We need to calculate the position of the spring at t = 1.5 s

Using position function

Put the value of t in the function

We need to calculate the velocity of the spring

Using position function

On differentiating

Put the value into the formula

Hence, The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards