Can someone please give me some hints on how to solve the following questions? Greatly appreciated...Cheers:)


During an experiment with a loaded spring, a student obtained various values for the periodic time, T, of the spring when different masses, M, were added to it.
In theory, the period, T, of a loaded spring varies with the mass attached to it according to the equation
T=2π √M/k where k is a constant for the particular type of spring used.

[a table was given with values of M/kg and T/s]

a. Use the equation to show that a graph of T2/s2 against M/kg should give a straight line.
b. (Copy the table) and tabulate the corresponding values for T2.
c. Plot the graph and useit to determine a value for k
d. The units for k are the Nm-1. Express these in terms of base units to show that they are consistent with the units for k obtained from the graph.

Hi punkprincess!

(a) T is proportional to the square root of M/k so T^2 is proportional to M/k and plotting them gives a straight line.
By the way, plotting transformed quantities in X and Y to get a straight line is still useful in 2008 in our computer-era, and is done commonly. People use to plot log(F) against 1/T if F depends on exp(-E/kT). One sees immediately in which interval the relation applies or if there are different E.

(b. and c) How shall I make a graph for you?

(d) N are kg*m/s^2 so mix and shake everything to get the result.
Investing some of your time in units would be very rewarding. Such checks are always useful, not just at homework.

I hope this is enough to help doing the rest by yourself.