The given differential equation is: [ \frac{d^2y}{dx^2} + 11 \frac{dy}{dx} + 24y = 0 ] Assume a solution of the form (y = e^{mx}). Then [ \frac{d^2y}{dx^2} = m^2 e^{mx}, \quad \frac{dy}{dx} = m e^{mx} ] Substitute into _____ ____ _______ __________ _________ _________.
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दो संरेख आवर्ती दोलनों की आवृत्ति है तथा उनके आयाम a1 एवं a2 और प्रारंभिक कलाएं क्रमशः
एवं
हैं। सिद्ध करें कि यदि इन दोलनों को अध्यारोपित किया जाए तो परिणामी गति का आयाम (a1 - a2) होगा। यदि
एवं
हो तो परिणामी आयाम का मान क्या होगा?
A particle A of mass moving along the x-axis with speed
collides elastically with a particle B of equal mass which is initially at rest. After the collision, particle A moves at an angle of
above the x-axis. Calculate the velocities of the two particles after the collision.
A girl of mass stands in an elevator. Obtain the force which the floor of the lift exerts on the girl
i) when the lift has an upward acceleration of ; ii) when the lift is rising at constant speed and iii) when the lift has a downward acceleration of
. Draw the free body diagram. Take
.
एक वक्र को निम्नलिखित प्राचलिक समीकरणों (parametric equations) द्वारा निरूपित किया जाता है :
बिन्दु पर इस वक्र पर एकक स्पर्शी सदिश ज्ञात करें।
Two collinear harmonic oscillations, each of frequency , have amplitudes, a1 and a2 and initial phases,
and
, respectively. Show that, when these oscillations are superposed, the amplitude of the resultant motion is equal to (a1 - a2). What will be the value of the resultant amplitude when
and
.
An object undergoes SHM with frequency . The initial displacement is
and the initial velocity is
. Calculate the amplitude, maximum velocity and maximum acceleration of the object.
A uniform disk of mass and radius
is initially at rest on a frictionless vertical axle. A constant tangential force of
is applied at the edge of the disk for
. Determine the i) the angular acceleration of the disk ii) the angular speed after
iii) the angular momentum of the disk after
, and iv) the rotational kinetic energy after
.