Question

1. Imagine you have two simple harmonic oscillators. Oscillator 1 is characterized by k1 10 kg s-2 and oscillator 2 by k25 kg s-2. The oscillators are displaced by the (a) If they each oscillate with a 1 kg mass, what is the period for the oscillators to (b) For some initial displacement d, where do the oscillators first come back into same amount in the same direction and are released together (in phase). come back into phase? phase?

Answer 1

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In this case we know that because T_1 2 x squareroot m/mu = 2x squareroot 1/10 = 2x/ squareroot 10 T_1 = 2 x squareroot m/mu = 2x/ squareroot 5 Phase = wt emptyset_1 - phi_1 = ? phase = emptyset_1 = 2x/T_1 t emptyset_2 = 2x/T_2 t emptyset_2 - emptyset_1 = 2 x rightdoublearrow 2x times squareroot 10 t/2x - 2x times squareroot 5 t/2x = 2x rightsinglearrow t (squareroot 10 - squareroot 5) = 2 x t = 2x/squareroot 10 - squareroot 5 (2) Let initial displacement given in the question = M phase due to this = 2x/lambda M rightdoublearrow emptyset_2 - emptyset_1: 2 x + 2x/lambda M t(squareroot 10 squareroot 5) = 2 x (1 + m) t = 2x/(squareroot 10 - squareroot 5)