Question

Problem1 A speaker is modeled with the system model given in the equations below. 2 m (x) + c(x) + kx = Kyi V(t) = L(i) + Ri + Kc(x) Given that the following constants, m- 2E-3 Kg, c 30 N.s/m, k 1.25E+5 N/m, K- Ke 2.5 Vls.m, L-0.02E-3 Henries (H) and R- 2 and the () indicate time derivatives, Find the maximum displacement, Xmax, when the speaker is given an input of V(t)-sin(2ft) when the frequency is varied between 100 Hz and 1500 Hz in steps of 200 Hz. Plot Xmax vs. Frequency, Xmax is the maximum steady state displacement from the simulation. Note: Let the simulation run for several cycles and find the maximum voltage using max0 function. As the system requires several cycles to get to the steady state response, remove the first few cycles when determining the maximum. To find the maximum of after discarding the first 20 points in an array, R, use max(R(20:end)). This will compute the maximum from 20th value in the array to the end. 0

Answer 1

on substituting the equations in one another for di/dt and completely obtaining the equation in dx/dt  

ヂR det 2-5 oox 2) (1 5xd) t12de o)冖.slt (20 sn)

Let C-BBanoot

6250u a3 62500 ot -18.817

If the initial values are given the constants are found and the graph can be plot with Matlab with frequency range as (100:200:1500) range is specified as per the requirement in the question.