Calculate the spring constant of oscillating mass on a spring colliding with a wall

Click For Summary
SUMMARY

The forum discussion centers on calculating the spring constant (k) for a mass-spring system where a block of mass 0.9 kg oscillates and collides elastically with a wall. The total time for one oscillation is given as 0.2 seconds. The calculations presented lead to a derived spring constant of 400 N/cm, while the expected answer is 100 N/m. The discrepancy arises from assumptions about the collision dynamics and the interpretation of the oscillation period, particularly regarding the elastic collision and the phase of motion.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of elastic collisions and their effects on motion
  • Familiarity with the equations of motion for oscillating systems
  • Ability to manipulate trigonometric functions in the context of SHM
NEXT STEPS
  • Study the derivation of the spring constant using the formula k = m(ω²) where ω = 2π/T
  • Learn about the effects of elastic collisions on oscillating systems
  • Explore the concept of phase difference in SHM and its impact on calculations
  • Investigate the relationship between amplitude, period, and spring constant in SHM
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in dynamics or oscillatory systems will benefit from this discussion, particularly those focusing on spring mechanics and collision theory.

  • #31
But a rather curious coincidence:
If I go by my first interpretation:
Aurelius120 said:
My interpretation was that the given diagram was of the relaxed spring (at ##0##) which would be compressed to left ##(-A)## and released. The wall being on the right ##(+A/2)##. That means one oscillation will be $$(-A)\rightarrow 0\rightarrow \frac{+A}{2} \rightarrow (-A)$$
Period of motion =0.2s given in question is time for ##(-A)\rightarrow 0 \rightarrow \frac{+A}{2} \rightarrow (-A)##
Then $$-A\cos (\omega t)=\frac{+A}{2}$$
$$\implies -\sqrt 2 \cos (\omega t)=\frac{+1}{\sqrt 2}$$
$$\implies \cos (\omega t)=\frac{-1}{2} \implies \omega t=\frac{2\pi}{3}$$
According to question time period of oscillation, 2t=0.2s therefore $$2\omega t= 0.2\omega = \frac{4\pi}{3}$$
This is the same incorrect answer I obtained in POST(1,11,22) and therefore this method is equivalent to that.

Period of motion =0.2s given in question is time for##(-A)\rightarrow 0 \rightarrow \frac{+A}{2} ##
Here I take t = 0.2s


Then, $$\omega t=0.2 \omega=\frac{2\pi}{3}\implies \frac{k}{0.9}=\frac{4\pi^2}{0.6^2}$$
Now this gives the correct answer.

This could either be a coincidence or even my initial interpretation is correct if period of motion in the question refers to time taken before first collision. [(-A) to (+A/2)]Could this question have two meanings? (POST 28)
 
Physics news on Phys.org
  • #32
Aurelius120 said:
before first collision. [(-A) to (+A/2)]
For the third time, it is not [(-A) to (+A/2)].
"Spring compressed to √2cm. "
A = √2cm.
"Block at 1/√2cm from wall."
Block starts at A/2 from wall; equilibrium is A from starting position, so A/2 to the right of the wall. The motion is an oscillation between -A and -A/2.
 
Last edited:

Similar threads

  • · Replies 40 ·
2
Replies
40
Views
5K
Replies
9
Views
2K
Replies
7
Views
1K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
17
Views
3K
Replies
24
Views
4K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
1
Views
1K
  • · Replies 32 ·
2
Replies
32
Views
2K