Question

obtain differential equations of linear shm​

Answer 1

Answer:

velocity of linear shm is given by,

v = w√(A²-x²) ...... (1)

where, v = velocity

w = omega(angular velocity)

A = acceleration

and x = displacement

as we know, v = dx/dt

so by substituting it in eq. 1

we get, dx/dt = w√(A²-x²)

dx/√(A²-x²) = wdt

now integrating it on both sides

€{dx/√(A²-x²)} = w€dt [ w is constant]

where € is integrating sine,,, I hope u understand

so now as we know it's a mathematical formula, we get, sin^-1(x/A) = wt+c [c=integrating constant]

x/A = sin(wt+c)

and x = Asin(wt+c)

this is the expression for displacement of linear shm

where c is is integrating constant called as initial phase and u have to take it as alpha in reality. so c = alpha

so,, x = Asin(wt+alpha)

so there are two cases,,

case 1 when particle is at mean position at time

t = 0, then x(displacement) = 0

so, 0 = Asin(0+alpha)

0 = Asin(alpha)

we know, A = 0 [impossible]×

so, sin(alpha) = 0

that's why,, alpha = 0

so eq. will be,, x = Asinwt

case 2 when particle is at extream position at time to = 0, then x = A

so, A = Asin(0+alpha)

1 = sin(alpha)

that's why,, alpha = π/2

so eq. will be,, x = Asin(wt+π/2)

x = Asin(π/2+wt)

x = Acoswt

Answer 2

Answer:

kaise bhare

deleting form yrr