Question

. Consider a weakly damped oscillator that is being driven by the periodic rectangular pulses shown in the following figure. Let the natural period of the oscillator beTo-3 and the damping constant be β = 0.1. Let the pulse last for a time Δτ= 1.5 and have a height fmax -5. Calculate the first four Fourier coefficient An for the long-term motion x(t) of the oscillator, assuming that the relation between the drive period τ and the natural period τοΒ 2 TT x(t)- An cos(nat om) n=0 f(t) T/2> AT /2 AT/2

Answer 1

Solution Equabion of motion of the oseiliatore 1s ton-蚁굿 < 4Z f(ら max , ot h enoise MD 2 ケー。 2- 2 Sin (nos) -4

2.2レ o heve An-2. 2 Δで 2. 2 n Lo て 2. T1wて 2

4t/2 m ax 乙 2x Cos 2. nwて 2 て nwr Fcos Sin S

て 02て 48.max Sim ( no △て A, 2. 2 て 2 て 6 一。

ent e 5% (n = 30 2. 2. 0 ane e o 30 si (Ir = 0.635 2. 几 n2 A2 = sin( 1 5 す"75. 0, 659 ·ヤー100