Question

A mass is suspended on a spring, pulled downward from its equilibrium position, and released. Assume that t = 0 when the spring is released, and the frequency of oscillation is w. Assume a vertical coordinate system in which the coordinate y points upward (see diagram at left).

Match the following physical quantities with their functional form.

Vertical Acceleration d^2y/dt^2 Vertical Velocity dy/dt Vertical position y Total Energy

A.	cos wt
B.	-sin wt
C.	Constant
D.	sin wt
E.	-cos (wt)

Answer 1

When released the body has maximum acceleration and accelerates upwards hence the function of acceleration
is cos(wt)

Vertical Acceleration d^2y/dt^2 ----> a) cos(wt)

Vertical velocity is minimum and increases sinosoidally as the body moves upward so the function is
sin(wt)

Vertical Velocity dy/dt -----> d)sin(wt)

Vertical position is at a minimum (negative extreme if mean position is taken as zero)
and increases sinosoidally hence the function describing the motion is
-cos(wt)

Vertical position y -----> e)-cos(wt)

Total energy is a constant.
It is the sum of kinetic and potential energy; though energy changes form from kinetic to potential and vice-versa
their sum is a constant.