Simple Harmonic Motion Question.

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.
  • #1

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)[tex]\sqrt{m/k}[/tex]

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.
 
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  • #2
well do you know how to find force due to a spring?
 
  • #3
cupid.callin said:
well do you know how to find force due to a spring?

Are you talking about hooke's law? F=-kx
 
  • #4
yes!

Now, which force do you think is responsible for the decrease in height of mass (not -kx one)!
 
  • #5
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..
 
  • #6
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?
 
  • #7
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
Got the answer!

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.

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