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A thin rod of length 2b and mass m is suspended by its two ends with two identical vertical springs (force constant k) that are attached to the horizontal ceiling. Assuming that the whole system is constrained to move in just the one vertical plane, find the normal frequencies and normal modes of small oscillations. Describe and explain the normal modes. [Hint: It is crucial to make a wise choice of generalized coordinates. One possibility would be, r, (phi) and (alpha), where r and (phi) specify the position of the rod's CM relative to an origin half way between the springs on the ceiling, and (alpha) is the angle of tilt of the rod. Be careful when writing down the potential energy.]
Damping is negligible for a 0.125-kg object hanging from a light, 6.30-N/m spring. Find a lower frequency and a higher frequency
Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed vi; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in t..
A space probe is launched from Earth, headed for deep space. At a distance of 15,000 miles from the Earth's center, What is the size of the force when it is at 30,000 miles from the Earth's center
A battery has an emf and an internal resistance . When the battery is connected to a 25 resistor, the current through the battery is 0.65 . When the battery is connected to 60 resistor, the current is 0.45 .
The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of 11.3 W. What is HooRU\'s temperature
In Niels Bohr's 1913 model of the atom, the electron is in a circular orbit around a nucleus. What is the magnitude of the magnetic moment due to the electron's motion
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Calculate the threshold frequency and wavelength for photoelectric effect from magnesium
a 190 pf capacitor and a 760 pf capacitor are both charged to 2.4 kv. they are then disconnected from the voltage
An aluminum plate has a length of 0.12 m and a width of 0.10 m at 25 °C. what is the change in the area of the plate as a result of the increase in temperature
When the Apollo astronauts were orbiting around the Moon at low altitude, What is the effect of a mascon on the orbital motion
The tension in a ligament in the human knee is approximately proportional to the extension of the ligament, What is the tension in this ligament when it is stretched by 0.67 cm
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