You run to the foot of the portcullis. In front of it you find two one-kilogram

Question

You run to the foot of the portcullis. In front of it you find two one-kilogram masses, five 1 gram masses, a one meter length of rope, and a selection of springs labeled 1 N/m, 10 N/m, and 100 N/m. A complicated looking locking mechanism has two hooks protruding from it. A small copper plaque says “Match the frequencies and raise the gate!” It also bears a diagram of a mass on a spring and a pendulum swinging side by side. From the available selection of masses and springs and the section of rope, can you build a pendulum and a mass on a spring such that you can find an angular frequency that matches and open the gate?

Explanation / Answer

Time Period of pendulum = 2*pi*sqrt(L/g)

Time period of spring mass system = 2*pi*sqrt(m/k)

both need to be equal for the gate to open.

=> L/g = m/k

=> 1/10 = m/k

Now, we can pick m = 1 kg and k = 10N/m to achieve this.

And for pendulum pick any mass with the 1m rope, time period would be the same.

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