How to Calculate the Spring Constant for Simple Harmonic Motion?

In summary, the conversation revolves around finding the spring constant and time period for a vertical spring with a 2kg weight hanging from it. The participants discuss using different equations and methods to calculate the spring constant, with one eventually suggesting using the second law of dynamics. The correct answer is determined to be 10 seconds for 10 cycles.
  • #1
physics noob
41
0
simple harmonic motion ?

hey guys, I am having troube with this problem

a vertical spring stretches .25m when a 2kg weight is hung from it. If that weight were oscillating up and down, how long would it take to complete 10 cycles?

so first i tried to find k by using PEi + KEi + PE(spring)i =PEf etc

so 2kg(.25m)(9.8) = .5(k)(.25)^2

so k= 156.8

then finding T T= 2(pi) sqroot(m/k)

so i get T= .709 * 10 oscillations = 7.1sec

correct answer is 10sec, meaning T must equal 1sec, which means k should equal somewhere around 78 or 79 ...working backwards...
i don't see how they get this value...any help is greatly appriciated THANKS
 
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  • #2
Hmm. Why can't you get the "k" value from the second law of dynamics applied to the spring-mass system...?

Daniel.
 
  • #3
hahaha, right on man, thanks! also thanks for not making me look like an idiot, i totally spaced using F=ma,,,,,however my question still remains, is it possible using MEi = MEf to obtain spring constant? thanks again for the quick help...
 
  • #4
physics noob said:
a vertical spring stretches .25m when a 2kg weight is hung from it.
From that fact and Hooke's law you should be able to calculate the spring constant.
 

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point with a constant amplitude and a fixed period. It is one of the most fundamental and widely studied phenomena in physics.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x(t) = A cos(ωt + φ), where x is the displacement of the object at time t, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation describes the position of an object undergoing simple harmonic motion as a function of time.

What is the difference between simple harmonic motion and periodic motion?

Simple harmonic motion is a specific type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium. Other types of periodic motion may have different restoring forces, such as gravitational or elastic forces. Simple harmonic motion is also characterized by a fixed period, whereas other types of periodic motion may have variable periods.

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

Some common examples of simple harmonic motion include a mass on a spring bouncing up and down, a pendulum swinging back and forth, and a bobber on a fishing line moving up and down in water. Simple harmonic motion can also be observed in the motion of molecules in gases and the vibrations of atoms in a solid.

How is simple harmonic motion related to Hooke's law?

Hooke's law states that the force needed to extend or compress a spring is directly proportional to the distance it is stretched or compressed. This is the same relationship as the restoring force in simple harmonic motion, which is why simple harmonic motion is often referred to as Hooke's law motion.

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