Problem 4
determine \(\omega_{0}, R,\) and \(\delta\) so as to write the given expression in the form \(u=R \cos \left(\omega_{0} t-\delta\right)\) $$ u=-2 \cos \pi t-3 \sin \pi t $$
Problem 5
use Euler’s formula to write the given expression in the form a + ib. $$ 2^{1-i} $$
Problem 5
Find the general solution of the given differential equation. $$ y^{\prime \prime}+5 y^{\prime}=0 $$
Problem 5
In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. \(f(t)=3 t-5, \quad g(t)=9 t-15\)
Problem 5
find the Wronskian of the given pair of functions. $$ e^{t} \sin t, \quad e^{t} \cos t $$
Problem 5
In each of Problems 1 through 10 find the general solution of the given differential equation. \(y^{\prime \prime}-2 y^{\prime}+10 y=0\)
Problem 5
A mass weighing 4 lb stretches a spring 1.5 in. The mass is displaced 2 in. in the positive direction from its equilibrium position and released with no initial velocity. Assuming that there is no damping and that the mass is acted on by an external force of \(2 \cos 3 t\) lb, formulate the initial value problem describing the motion of the mass.
Problem 6
A mass of \(5 \mathrm{kg}\) stretches a spring \(10 \mathrm{cm} .\) The mass is acted on by an external force of \(10 \mathrm{sin}(t / 2) \mathrm{N}\) (newtons) and moves in a medium that imparts a viscous force of \(2 \mathrm{N}\) when the speed of the mass is \(4 \mathrm{cm} / \mathrm{sec} .\) If the mass is set in motion from its equilibrium position with an initial velocity of \(3 \mathrm{cm} / \mathrm{sec}\), formulate the initial value problem describing the motion of the mass.
Problem 6
use Euler’s formula to write the given expression in the form a + ib. $$ \pi^{-1+2 i} $$
Problem 6
In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. \(f(t)=t, \quad g(t)=t^{-1}\)
