Question

A spring stretches 4cm when a 5g mass is hung from it. if a total mass of 20g attached to this spring oscillates in simple harmonic motion, calculate the period of motion.

Answer 1

The period of oscillation for a 20g mass attached to a spring, which stretches 4cm with a 5g mass, is approximately 0.81 seconds.

Step-by-step explanation:

The question asks to calculate the period of motion for a 20g mass attached to a spring, oscillating in simple harmonic motion (SHM).

From the information given, we know that the spring stretches 4cm (0.04m) when a 5g mass is hung from it.

First, let's determine the spring constant (k) using Hooke's Law: F = kx, where F is the force applied (in newtons) and x is the displacement (in meters).

The force caused by the 5g mass is mg, where m is the mass (0.005kg) and g is acceleration due to gravity (9.8 m/s2).

F = (0.005kg)(9.8m/s2) = 0.049N
k = F/x = 0.049N/0.04m = 1.225 N/m

Now, we can calculate the period (T) using the formula for the period of a mass-spring system: T = 2π√(m/k), where m is the mass of the object attached to the spring.

For a 20g mass, we have:

m = 0.020kg
T = 2π√(0.020kg/1.225 N/m)

= 2π√(0.01639kg/Nm)

≈ 0.81 s

Thus, the period of oscillation for the 20g mass attached to this spring is approximately 0.81 seconds.