Aurelius120
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But a rather curious coincidence:
If I go by my first interpretation:
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)
If I go by my first interpretation:
Period of motion =0.2s given in question is time for ##(-A)\rightarrow 0 \rightarrow \frac{+A}{2} \rightarrow (-A)##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 $$(-A)\rightarrow 0\rightarrow \frac{+A}{2} \rightarrow (-A)$$
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)