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

Click For Summary
The discussion revolves around calculating the spring constant (k) for a mass-spring system where the mass collides elastically with a wall. The total oscillation time is given as 0.2 seconds, and participants debate the implications of the wall collision on the calculations. The original calculations led to a spring constant of 400 N/cm, while the expected answer is 100 N/m. Key points include the need to account for the elastic collision and the correct interpretation of the motion phases, with emphasis on using the appropriate equations for maximum displacement and time intervals. Clarifications on the initial conditions and assumptions about the collision are essential for arriving at the correct value of k.
  • #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
4K
Replies
9
Views
2K
Replies
7
Views
1K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
17
Views
2K
Replies
24
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
1
Views
975
  • · Replies 32 ·
2
Replies
32
Views
2K