Homework Statement
this problem was on my finals and i stared at it for 30 mins straight and still didn't figure it out and now it just bothers me that i don't know how to do the first problem on my final exam.
"find the general solution to the dfq"
xy'+xy= 1-y
Homework Equations...
thanks for responding, Lets see if i have the yp's correct
yp = (At^2+Bt+c)e^-t
y'p = (2At + B)e^-t -(At^2+Bt+c)e^-t
y''p = 2Ae^-t - (2At + B)e^-t - (2At+B)e^-t -(At^2+Bt+c)e^-t
Homework Statement
Find the general solution to the diff equation using undetermined coefficients
y''-2y'-3y = 3te^-1
Homework Equations
The Attempt at a Solution
r^2 - 2r -3 = 0
r = -1, 3
so y = c1 e^-t + c2e^3t + yp
since e^-t already exists as a solution, i have to...
Homework Statement
Find y2 given
t^2y'' + 3ty' + y = 0 y1(t) = 1/t
Homework Equations
The Attempt at a Solution
i found y, y' and y'' and plugged it back in to the Differential equation,
after doing some work, i'm basicly down to
tv''+v' = 0
where y2 = v/t
so u =...
Homework Statement
Solving this differential equation
ty' + 2y = t^2 - t + 1
Homework Equations
Its linear so i set it up in linear form
y' + y(2/t) = t - 1 +1/t
The Attempt at a Solution
the integrating factor (u) = e ^ integral (ydt) = e^ integral (2dt/t)...
Here's the...
Homework Statement
There is a large bed floating in sea with the density of 765 kg/m^3. What fraction of the bed's volume will be under the surface of the water? The density of sea water is 1035 kg/m^3.
Homework Equations
Fb = Density * v * gravity
The Attempt at a Solution
I know...
Homework Statement
A small cube (m=0.450 kg) is at a height of 393 cm up a frictionless track which has a loop of radius, R = 58.95 cm at the bottom. The cube starts from rest and slides freely down the ramp and around the loop. Find the speed of the block when it is at the top of the loop...
Isn't that what i did? B = Density * V * g and like you said water is fairly constant, so V = B/g
which is 34N/9.8 = 3.47 which is the volume of the object, right?
So now i can do D = m/v for the density of the object given m of object is 341/9.8.
And i just confused myself, we're ignoring the...
Homework Statement
An object weighing 341 N in air is immersed in water after being tied to a string connected to a force scale. The scale now reads 307 N. Calculate the density of the object.
Homework Equations
Fb=(density of the surrounding liquid)(V)(g)
The Attempt at a...
Homework Statement
Find the minimum diameter of an l = 17.2 m long steel wire that will stretch no more than 7.38 mm when a mass of 323 kg is hung on the lower end. (Hint: The Young's modulus of steel is 200.0 GPa.)
Homework Equations
Youngs = (Force / Area) / (change L / L)...
i got 16.97 as n. it works because .96^17 = ~ 0.499
So if thats true, 0.88 which is the period * 16.97 which gives me 14.94 seconds.
This makes sense except the answer's still wrong?
Homework Statement
A mass M is suspended from a spring and oscillates with a period of 0.880 s. Each complete oscillation results in an amplitude reduction of a factor of 0.96 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the...
Homework Statement
On a roller coaster ride the total mass of the cart - with passengers included - is 280 kg. Peak K is at 46.0 m above the ground, peak L is at 21.5 m. The speed of the cart at K is 17.1 m/s, at L it is 12.8 m/s. How much energy is lost due to friction between the two peaks...
I don't think that works.
Remember gravity is still pulling on the block as it travels up the loop, so the speed has to be different from when it entered the loop.
I believe it has something to do w/ conservation of energy, i just don't know where to start
Homework Statement
A small cube (m=0.450 kg) is at a height of 393 cm up a frictionless track which has a loop of radius, R = 58.95 cm at the bottom. The cube starts from rest and slides freely down the ramp and around the loop. Find the speed of the block when it is at the top of the loop...
Homework Statement
A solid sphere of uniform density (weight = 3.2 lbs starts from rest and rolls down a ramp (H = 1.57 m, q = 18.3°.)
Find the speed of the sphere's CM when it reaches the bottom of the ramp.
haha sorry bout that....
Homework Equations
see below
The Attempt at...
Homework Statement
Four blocks are on a horizontal surface. The blocks are connected by thin strings with tensions Tx, Ty, Tz. The masses of the blocks are A=22.0 kg, B=21.0 kg, C=17.0 kg, D=27.0 kg. Two forces, F1=83.0N and F2=50.0N act on the masses as shown. Assume that the friction...