A5.30kg block hangs from a spring with a spring constant 1700 n/m. the block is pulled down 4.50cm from the equilibrium position and given an initial velocity of 1.70 m/s back toward equilibrium. a) what is the frequency of the motion (units: hz) b) what is the amplitude (units: m) c) what is the total mechanical energy of the motion (units: j)

To solve this problem it is necessary to apply the concepts related to the frequency in a spring, the conservation of energy and the total mechanical energy in the body (kinetic or potential as the case may be)

PART A) By definition the frequency in a spring is given by the equation

Where,

m = mass

k = spring constant

Our values are,

k=1700N/m

m=5.3 kg

Replacing,

PART B) To solve this section it is necessary to apply the concepts related to the conservation of energy both potential (simple harmonic) and kinetic in the spring.

Where,

k = Spring constant

m = mass

y = Vertical compression

v = Velocity

This expression is equivalent to,

Our values are given as,

k=1700 N/m

V=1.70 m/s

y=0.045m

m=5.3 kg

Replacing we have,

Solving for A,

PART C) Finally, the total mechanical energy is given by the equation