Nice — let’s solve it by hand. We have linear ODE with constant coefficients $$ _________ ____ ___ ___ ________.
____ _____ ___ _____ _____ _______ __________ __________ ______ ____ ______ ________.
_____ ______ _________ ________ __________ ________ _____.
_______ __________ ________ _________ ____ _________ _____.
______ ______ _____ _____ ________ _____ __________ __________ ___ _____ ____ __________.
______ _______ ______ _________ _____ ________ ________ ___ _______.
________ _______ _____ ________ __________ __________.
_______ ______ ________ ________ ___.
____ ___ ________ ________ _________ _________ ______ ____ __________ __________ _________.
________.
Get Full Answer on WhatsApp
The equation of transverse wave on a rope is
where y and x are measured in cm and t is expressed in second. Calculate the maximum speed of a particle on the rope.
किसी अवमंदित आवर्त दोलक का गति समीकरण निम्नलिखित है :
जहां m = 0.25kg, y = 0.05kgs-1 तथा k = 70Nm-1 है। (i) दोलन काल, (ii) दोलनों
की संख्या जिसके बाद आयाम का मान उसके आरंभिक मान का आधा रह जाता है, (iii) दोलनों की संख्या जिसके बाद दोलक की यांत्रिक ऊर्जा का मान उसके आरंभिक मान का आधा रह जाता है, परिकलित करें।
Solve the following ordinary differential equations:
a)
Solve the following ordinary differential equations:
For a damped harmonic oscillation, the equation of motion is
Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, and (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value.
A simple harmonic oscillator has amplitude 15 cm and it completes 100 oscillations in 50 s. (i) Calculate its time period and angular frequency. (ii) If the initial phase is /2, write expressions for its displacement and velocity. (iii) Calculate the values of maximum velocity and acceleration.
A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in 10s. What would be the power required?
b) A proton undergoes a head on elastic collision with a particle of unknown mass Initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the ratio of the mass of the unknown particle with respect to the mass of the proton. c) The planet Jupiter has an elliptical orbit e =.05 and a semi major axis of 7.8 10 11 m . Find the energy of the planet and the perihelion and aphelion distances