Consider a mass is free to slide along the table (see s amplitude (0.2 meters),

Question

Consider a mass is free to slide along the table (see s amplitude (0.2 meters), period (S to the spring in this problem. mass on a spring system oriented along a horizontal table. The table is frictionless and the f ide 15 in your Simple Harmonic Motion Notes). You know that Consider a simple pendulum swinging at a constant rate near the surface of the earth (see slide 20 in your Simple Harmonic Motion Notes). Assume that this system has the same amplitude, period, and total energy as the mass on a spring system described above. Find the length of string that attaches the mass to the pivot point on the ceiling. Grade:

Explanation / Answer

First Question -

At the amplitude, x = 0.20 m, the total energy of the spring-mass system is the potential energy stored in the system.

Means -

Etotal = (1/2)*k*x^2

given, x = 0.20 m, Etotal = 10 J

Put these values in the above -

10 = 0.5*k*0.20^2

=> k = 10 / (0.5*0.20^2) = 500 N/m

Now time period of a spring-mass system -

T = 2*pi*sqrt[m/k]

=> 5 = 2*3.141*sqrt[m/k]

=> sqrt[m/k] = 0.7959

=> m/k = 0.6335

=> m = 0.6335*500 = 316.7 kg

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