Question

When a 0.350 kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?

a) Draw a diagram representing the scenario

b) Solve the equation symbolically (without numbers)

c) Solve the equation with numbers

d) State any relevant concepts

Answer 1

given
m = 0.35 kg
delta_y = 12.0 cm = 0.120 m
let k is the spring constant.

a) sprring placed vertically and connected to a package.

b) in the equilibrium,

F_spring = Fg

k*delta_y = m*g

k/m = g/delta_y

angular frequency, w = sqrt(k/m)

and time period, T = 2*pi/w

= 2*pi/sqrt(k/m)

= 2*pi/sqrt(g/delta_y)

c) T = 2*pi/sqrt(9.8/0.120)

= 0.695 s

d) here the total mechaincal energy is concerved when the package makes oscillations.

when the pakcage is at rest initially the net force acting on the pakage is zero.