Question

1) An object of mass 3200g is attached to a string with a spring constant 29N/m and set into motion. When the object is 1.74m away from its equilibrium position, it is observed to be moving with speed 2.4m/s. What is the amplitude of the object's oscillation?

2) A small object with mass 320g is attached to a spring constant of 25.4N/m. If the object is set into oscillation, how many cycles of oscillation will it complete each minute?

Answer 1

here,

1)

mass of object , m = 3200 g = 3.2 kg

spring constant , K = 29 N/m

at x1 = 1.74 m , v1 = 2.4 m/s

let the amplitude of motion be A

using conservation of energy

0.5 * K * A^2 = 0.5 * m * v1^2 + 0.5 * K * x1^2

29 * A^2 = 3.2 * 2.4^2 + 29 * 1.74^2

A = 1.91 m

the amplitude of motion is 1.91 m

2)

mass of object , m = 320 g = 0.32 kg

spring constant , K = 25.4 N/m

the frequeny of oscillation , f = 1/2pi * sqrt(K/m)

f = 1/2pi * sqrt(25.4 /0.32)

f = 1.42 rev/s

f = 1.42 * 60 rev/min

f = 85.1 rev/min