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1. Help with Oscillations Problem

Homework Statement A 253 g oscillator has a speed of 89.28 cm/s when the displacement is 2.79 cm and a speed of 70.95 cm/s when the displacement is 6.56 cm. What is the oscillator's maximum speed? Homework Equations The Attempt at a Solution well, I haven't really attempted a...
2. Improper integrals with infinite discontinuities

Homework Statement \int\frac{13}{(x-8)^2}dx Homework Equations it is integrated from 7 to 9 and i am aware that there is an infinite discontinuity at x=8 so we have to take the limit from both sides individually. The Attempt at a Solution The only thing I can think that I might...
3. How much torque must the pin exert to keep the rod from rotating?

Homework Statement How much torque must the pin exert to keep the rod from rotating? (L=1.011m , M=3kg , m = .301kg) So I am guessing the point of rotation is the pin?? But then how does the pin exert any torque if it is at the point of rotation? I'm not quite sure there is a...
4. Gravitational forces

I have this problem i have been trying to solve and can't seem to get it right. The question states: The space shuttle is in orbit 396.9 km above the surface of the earth. What is the gravitational force on a 0.64 kg sphere inside the space shuttle? mass earth = 5.98x10^24 kg radius of...
5. Trigonometric substitution

I’ve got this tricky trig substitution that I’ve been trying to do as for my Calc II class. I think that I’ve done the substitution part right I just have no idea where to go from here. I’ve tried many routes including integrating by parts as well. Please help me thank you...
6. Area of a curve revolved about x-axis

I'm pretty sure i'm setting this up right i just get stuck when i need to integrate it the equation is y=e^x and rotated around the x axis I've attached the question can someone help me thanks