A mass is hung from a spring; it is then pulled down and released. The mass oscillates (bounces) up and down with a certain time period . The graph below shows how the period of oscillation depends upon the mass for different numbers of springs attached to the mass in parallel to each other. Note: all the springs are identical, each with spring constant .
(a) What equation shows the correct dependence of period on and , and justify your choice using data from the graph.
$T=2\sqrt\frac{k}{m}$ $T=2\sqrt\frac{m}{k}$ $T=2\sqrt{mk}$ $T=2\sqrt\frac{1}{mk}$
Graph shows the Period increasing as the Mass increases, for each of the different number of springs. i.e. Period is directly proportional to the Mass. Each of the equations:
$T=2\sqrt\frac{m}{k}$ $T=2\sqrt{mk}$
show a directly proportional relationship, the other 2 equations show an indirectly proportional relationship with Period decreasing as Mass increases; i believe.
So which of these two equations correctly represent the relationship presented in the graph?
The mass hanging off the spring is 6.0 kg.
(b) From the graph, determine the period of this spring-mass system. (Assume only one spring is used.)
9.6 seconds
(c) Calculate the number of oscillations that will pass during a 1 hour period. Give your answer to the nearest oscillation.
1 oscillation takes 9.6 seconds
Oscillations in 1 hour = $\frac{3600}{9.6} = 375$
Does that seem correct, question seems to suggest oscillations contains decimals?
The equivalent spring constant of $N$ identical springs connected in parallel is $N k$. The graph shows a relation that is the square root function (horizontal parabola). Therefore,
$ T = 2 \pi \sqrt{ \dfrac{m}{k} } $
is the correct choice, because, for $m = 1$, you have for one spring, $T = 4 $, and for $4$ springs $T = 2$. This means the period $T$ is inversely proportional to the square root of $k$.
The answers to parts (b) and (c) are correct.