You are given the task of opening an antiquated “light lock,” which is unlocked by shining red light pulses of a certain frequency for a long duration of time into a light sensor on the lock. You are given a red laser pointer, a spring of unstretched length L = 15.0 cm and spring constant k = 7.20 N/m, a sheet of steel (ρ = 7.60 g/cm³) that is 0.125 inches thick, and some tools. You come up with the idea to take a piece of the steel sheet (of mass m), cut a slot in it, and hang it from the spring. If you shine the laser through the slot and onto the sensor, and then stretch the spring and let it go, the steel plate will oscillate and cause the beam to pass through the slot periodically.

(a) Assuming the beam is passing through the slot (and onto the lock’s sensor) when the spring-mass system is in equilibrium, how is the frequency at which the light pulses hit the sensor related to the frequency of the spring/mass (i.e., steel plate) system.

(b) Based on your answer for (a), what should be the frequency of the spring/mass system if the unlocking frequency is 3.50 Hz?

(c) What should be the mass m of the steel plate?

(d) Calculate some reasonable dimensions for the steel plate (i.e., they should be consistent with the mass that is required for the spring-mass system). You may assume the material removed to make the slot in the steel plate is of negligible mass.