Question

A block of unknown mass is attached to a spring with a force constant of 6.50 N/m and undergoes simple harmonic motion with an amplitude of 10.0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 30 cm/s. Calculate a) the mass of the block, b) the period of the motion, and c) the maximum acceleration of the block.

Answer 1

given,

force constant

k = 6.5 N/m

Amplitude = A = 10 cm

a) using conserving of energy

`E = (1)/(2)kA^2`

`E = (1)/(2)* 6.5 * 0.1^2`

E = 32.5 m J

now,

`E = (1)/(2)kA^2+ (1)/(2)mv^2`

`E = (E)/(4)+ (1)/(2)mv^2`

`m= (3E)/(4)(2)/(v^2)`

`m= (3* 32.5 * 10^(-3))/(4)(2)/(0.3^2)`

m =0.542 Kg

b) time period of the motion

`T= 2\pi \sqrt{(m)/(K)}`

`T= 2\pi \sqrt{(0.542)/(6.50)}`

T = 1.814 s

c) F = m a and also

F = k A

now, computing both the formula

`a_(max) = (k A)/(m)`

`a_(max) = (6.58* 0.1)/(0.542)`

`a_(max) =1.21\ m/s^2`