# Simple Harmonic Motion Question.

• Student3.41
In summary, the conversation discusses finding the period of oscillations when a mass is displaced from equilibrium on a spring. Hooke's law and Newton's second law are referenced, and it is determined that the force of gravity is responsible for the decrease in height of the mass. The mass-to-spring constant ratio is found and used to calculate the period of oscillations.

## Homework Statement

When a mass is hung from a spring, the spring elongates by 10.6cm. What will the period of the resulting oscillations be if the mass is displaced from equilibrium?

## Homework Equations

T=2(pi)$$\sqrt{m/k}$$

## The Attempt at a Solution

I have no clue what do with this question, if I am not given a mass or spring constant. I tried using Newtons 2nd Law to find k but without knowing the mass I ended up with two unknowns.

well do you know how to find force due to a spring?

cupid.callin said:
well do you know how to find force due to a spring?

Are you talking about hooke's law? F=-kx

yes!

Now, which force do you think is responsible for the decrease in height of mass (not -kx one)!

cupid.callin said:
yes!

Now, which force do you think is responsible for the decrease in height of mass (not -kx one)!

Well the only other force acting on the object is gravity..

yes ... now as you will know that at point where net acc. on body will be zero ... Fnet = 0

can you figure out m/k now?

cupid.callin said:
yes ... now as you will know that at point where net acc. on body will be zero ... Fnet = 0

can you figure out m/k now?

Fnet=0
Fs-mg=0
kx=mg
x/g=m/k

(0.106/9.81)=m/k

=0.104= m/k

T=2(pi)square(0.104)root

Thanks! I was approaching the problem right, I just never noticed m/k=x/g... appreciate the help

Last edited:

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of oscillatory motion in which a system or object moves back and forth in a regular pattern around an equilibrium point. The motion is described by a sine or cosine function and is characterized by a constant amplitude and frequency.

## 2. What causes simple harmonic motion?

Simple harmonic motion is caused by a restoring force that is proportional to the displacement of the object from its equilibrium point. This restoring force can come from gravity, a spring, or any other force that follows Hooke's Law.

## 3. What is the difference between simple harmonic motion and periodic motion?

Simple harmonic motion refers to a specific type of periodic motion in which the displacement of the object follows a sine or cosine function. Periodic motion, on the other hand, refers to any motion that repeats itself over a regular interval of time.

## 4. What are some real-life examples of simple harmonic motion?

Some examples of simple harmonic motion in real-life include the motion of a pendulum, the oscillation of a mass on a spring, and the vibration of a guitar string. The motion of a swing and the movement of a mass attached to a rubber band also exhibit simple harmonic motion.

## 5. How is simple harmonic motion related to energy?

In simple harmonic motion, the total mechanical energy (potential energy + kinetic energy) of the system remains constant. As the object moves back and forth, its potential energy is converted to kinetic energy and vice versa. This energy conservation is a key characteristic of simple harmonic motion.