Write the particular time dependent solution of the undamped harmonic oscillator given that at time t=0, the spring is initially at its equilibrium with an initial velocity v_0 and identify each term in the expression. Also, write the form of the time dependent velocity and show that it obeys the initial conditions.

Tidal Friction

For the calculations below, note that the Moon's mass is about 1/80th of the Earth's, so the total mass of the Earth-Moon system is essentially the Earth's mass.

(a) Once the Earth is in synchronous rotation with the Moon's orbit, what will be the semimajor axis (in km) of the Moon's orbit? Will it be inside or outside the Earth's Hill sphere?

(b) How large (in angular diameter) will the Moon appear in the Earth's sky once it's in synchronous orbit?

can someone tell me the differences between “Free Undamped Motion”, “Free Damped Motion”, “Driven Undamped Motion”, or “Driven Damped Motion”

sample drawings will be helpful.

Error...

A jet with mass m = 6 × 104 kg jet accelerates down the runway for takeoff at 2 m/s2. 1)What is the net horizontal force on the airplane as it accelerates for takeoff?

2)What is the net vertical force on the airplane as it accelerates for takeoff?

3)Once off the ground, the plane climbs upward for 20 seconds. During this time, the vertical speed increases from zero to 20 m/s, while the horizontal speed increases from 80 m/s to 98 m/s. What is the net horizontal force on the airplane as it climbs upward?

4)What is the net vertical force on the airplane as it climbs upward?

5)After reaching cruising altitude, the plane levels off, keeping the horizontal speed constant, but smoothly reducing the vertical speed to zero, in 16 seconds. What is the net horizontal force on the airplane as it levels off?

6)What is the net vertical force on the airplane as it levels off?

Suppose 1.0 mol of an ideal gas is initially at P=4.0 atm and T=400 K. It is expanded irreversibly and adiabatically against a constant pressure of 1.0 atm until the volume has doubled.
(a) Calculate the final volume of the gas.
(b) Calculate w, q, and energy change ΔU of this process, in joules.
(c) Calculate the final temperature of the gas.
(d) Calculate the entropy change ΔS of the ideal gas in the process.
(e) What is the entropy change of the surroundings, ΔS_surr, during this process? Does the results in (c) and (d) in combination satisfy the second law of thermodynamics? Explain

An object with mass 70 kg moved in outer space. When it was at location <7, -35, -5> its speed was 5.0 m/s. A single constant force <210, 400, -150> N acted on the object while the object moved from location <7, -35, -5> m to location <11, -27, -8> m. Then a different single constant force <140, 250, 210> N acted on the object while the object moved from location <11, -27, -8> m to location <17, -31, -3> m. What is the speed of the object at this final location?

Two 15-cm-diameter metal disks separated by a 0.69-mm-thick piece of Pyrex glass are charged to a potential difference of 1100 V .

What is the surface charge density on the disks?

What is the surface charge density on the glass?

A grinding wheel is in the form of a uniform solid disk of radius 6.96 cm and mass 2.05 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.606 N · m that the motor exerts on the wheel.

(a) How long does the wheel take to reach its final operating speed of 1 190 rev/min?
  s

(b) Through how many revolutions does it turn while accelerating?
rev

If you know the mass of a star and an object

A stone is thrown with an initial velocity of 35.0 m/s at an angle of 37 degrees above the horizontal. Find: (a) its horizontal and vertical displacement after 0.55 s; (b) its velocity after 0.55 s (both magnitude and direction). (c) its maximum height and range.

The speed of a plane in the absence of wind is 500 km/hr. In the presence of a wind, in order to fly due north at a speed of 450 km/hr with respect to the ground, the pilot must point the plane in a direction 35^o east of due north. Which of the following vectors (in unit vector notation) describes the velocity of the wind with respect to the ground?

How are standing waves similar to beats and how are they different?

Typing only, no handwriting

The charges and coordinates of two charged particles held fixed in the xy plane are: q1=6.40 μC, x1=-8.100 cm, y1=5.600 cm, and q2=6.00 μC, x2=-4.652 cm, y2=10.013 cm, Find the magnitude and direction of the electrostatic force on q2. 1.1010×102 N 5.2000×101 deg You are correct. Your receipt no. is 157-5132 Help: Receipt Previous Tries What are the x and y coordinates of a third charge q3=3.80 μC, if the net electrostatic force on q2 is zero?