Aspring and mass system is set into motion by pulling the mass 3.50 cm from the equilibrium position and releasing it. this simple harmonic oscillator has a maximum speed of 26.0 cm/s. what is its speed when the displacement of the mass is 1.75 cm?

To develop this problem it is necessary to apply the concepts related to speed from the simple harmonic movement. We know that mathematically speed can be expressed as

Where,

= Angular velocity

A = Amplitude

x = Displacement

For the expression within the square root to be maximum then x must be equivalent to zero therefore

Reorganizing the equation to obtain the highest value of angular velocity we have to

Replacing with our values we have to

Finally the speed at the swing point equivalent to 1.75cm would be:

Therefore the speed when the displacement of the mass is 1.75cm would be 0.225m/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