Question: A mass M is free to slide along a frictionless rail. A pendulum of length ? and mass m hangs from M (see Fig.). Find

A mass M is free to slide along a frictionless rail. A pendulum of length ? and mass m hangs from M (see Fig.). Find the equations of motion. For small oscillations, find the normal modes and their frequencies. M m

M m

Step by Step Solution

★★★★★

3.45 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let a be the coordinate of M and let be the angle of the pendulum see Fig Then the position of the m... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

36-P-M-K (302).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

d (1-3); please show work. Once 1 2 3 Exhibit 6-10 Midwest Office Products: Five Orders 4 5 $610 500 1 56.100 5.000 10 10 56.100 5,000 10 10 Price Acquisition cost Number of cartons in order Number...

A bead is free to slide along a frictionless hoop of radius r. The plane of the hoop is horizontal, and the center of the hoop travels in a horizontal circle of radius R, with constant angular speed...

A mass M is free to slide down a frictionless plane inclined at angle ?. A pendulum of length ? and mass m hangs from M (see Fig.). Find the equations of motion. For small oscillations, find the...

A glider of mass m is free to slide along a horizontal air track. It is pushed against a launcher at one end of the track. Model the launcher as a light spring of force constant k compressed by a...

Strontium (Sr) is element 38 on the periodic table. A sample contains 5.77x1025 atoms of Sr. Calculate the amount of Sr. Submit mol Sr Show Approach Hide Tutor Steps

M.C. What is the average life expectancy? 60yrs. to 80yrs. 65yrs. to 90yrs. 75yrs. to 80yrs

Problem 3 : Compound pendulum attached to cart A rigid rod of length L , mass M and centroidal moment of inertia I G hangs from a pivot as shown. The angular displacement of the rod is . The base of...

Procedure I Data Table 1: Mass and Weight Object Mass in g Mass in kg Weight in N Wooden Friction block 31.1 0.031 0.30 Glass /sandpaper friction block 55.6 0.056 0.55 50 g hanging mass 50 0.05 0.49...

Judy is considering receiving either $20,000 of current salary or $40,000 of deferred compensation in 12 years. Her current tax rate is 33%, but she expects her tax rate to be 15% 12 years from now....

Take as much time needed to answer every single question. Just be sure to answer ead h question correctly and will write a wor iew about you afterwards! Do not rush and use the correct amount of...

6. Write a paper guided by the following requirements: a. Introduction: Write a brief introduction to the paper. b. Article Summary: Provide a brief summary of the Birkman (2008) article: HR...

Propose reagents and conditions for the following multistep syntheses. You may use any reagents necessary. Be sure to draw all isolable intermediates. ? Br.

Conventional thinking is that the incentive effects of budgeting systems are enhanced by Blank _ _ _ _ _ _ . Multiple choice question. having top management formulate most budgets. allowing employees...

A piston/cylinder of total 1 kg steel contains 0.5 kg ammonia at 1600 kPa, both masses at 120C. Some stops are placed that so a minimum volume is 0.02 m 3 , shown in Fig. P6.137. Now the whole system...

A 5-lbm aluminum radiator holds 2 lbm liquid R-134a at 10 F. The setup is brought indoors and heated with 220 Btu. Find the final temperature and the change in entropy of all the mass.

A piston/cylinder device keeping a constant pressure has 1 kg water at 20C and 1 kg of water at 100C, both at 500 kPa separated by a thin membrane, shown in Fig. P6.128. The membrane is broken and...

A car engine block receives 2 kW at its surface of 450 K from hot combustion gases at 1500 K. Near the cooling channel, the engine block transmits 2 kW out at its 400 K surface to the coolant flowing...

A heat pump with COP = 4 uses 1 kW of power input to heat a 25C room, drawing energy from the outside at 15C. Assume the high/low temperatures in the heat pump are 45C/0C. Find the total rates of...

What advantages does Industry 5.0 have for (a) staff, (b) senior management?

A rigid steel plate is supported by three posts of high-strength concrete each having an effective cross-sectional area A = 40,000 mm2 and length L = 2 m (see figure). Before the load P is applied,...

A capped cast-iron pipe is compressed by a brass rod, as shown. The nut is turned until it is just snug, then add an additional quarter turn to pre-compress the CI pipe. The pitch of the threads of...

An aluminum pipe has a length of 60 m at a temperature of 10C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (degrees Celsius) will the...

THIS IS NOT THE ANSWER : Basic EPS: $0.68 Diluted EPS: $0.58 On December 31, 2023, Chi Chow Company had outstanding 420,000 shares of common stock and 42,000 shares of 8% cumulative preferred stock...

Perteet Corporation's relevant range of activity is 7,500 units to 14,500 units. When it produces and sells 11,000 units, its average costs per unit are as follows: Average Cost per Unit Direct...

Required information [The following information applies to the questions displayed below.] On January 1, 2024, Splash City issues $430,000 of 8% bonds, due in 15 years, with interest payable...