Question: An object of mass m is hung from the base of an ideal spring that is suspended from the ceiling. The spring has a spring

An object of mass m is hung from the base of an ideal spring that is suspended from the ceiling. The spring has a spring constant k. The object is pulled down a distance D from equilibrium and released. Later, the same system is set oscillating by pulling the object down a distance 2D from equilibrium and then releasing it.
(a) How do the period and frequency of oscillation change when the initial displacement is increased from D to 2D?
(b) How does the total energy of oscillation change when the initial displacement is increased from D to 2D? Give the answer as a numerical ratio.
(c) The mass-spring system is set into oscillation a third time. This time the object is pulled down a distance of 2D and then given a push downward some more, so that it has an initial speed vi downward. How do the period and frequency of oscillation compare to those you found in part (a)?
(d) How does the total energy compare to when the object was released from rest at a displacement 2D?

Step by Step Solution

★★★★★

3.28 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Refer to Eqs 1020 Use conservation of energy and the fact that E A 2 Analyze 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)

956-P-M-L-M (1413).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

MAKE SURE ALL FORMULAS ARE CORRECTLY ENTERED MAKE SURE ALL FORMULAS ARE CORRECTLY ENTERED Jay Corporation has provided data from a two-year period to aid in planning. The Controller has asked you to...

A light spring with spring constant k1 is hung from an elevated support. From its lower end a second light spring is hung, which has spring constant k2. An object of mass m is hung at rest from the...

An object of mass M is held in place by an applied force F and a pulley system as shown in Figure P5.55. The pulleys are mass less and frictionless. Find (a) the tension in each section of rope, T1,...

A light string with a mass per unit length of 8.00 g/m has its ends tied to two walls separated by a distance equal to three fourths of the length of the string (Fig. P16.30) An object of mass m is...

Learning Goal: To use the equations of equilibrium to find unknown forces in two dimensions; understand the relationship between a spring's unloaded length, its displacement, and its loaded length;...

An object of mass 306 g is attached to the base of a spring, with spring constant 25 N/m, that is hanging from the ceiling. A pen is attached to the back of the object, so that it can write on a...

(13%) Problem 1: One kind of cuckoo clock keeps time by using a mass bouncing on a spring, usually something cute like a cherub in a chair. DA What is the force constant, in newtons per meter, needed...

CONCEPTUAL Physics PRACTICE PAGE Chapter 4 Newton's Second Law of Motion Converting Mass to Weight Objects with mass also have weight (although they can be weightless under special conditions). If...

Lesson 6 : Part A: (The Concepts): True/False: Answer each question given below by answering if the question is true or false. Include your explanation for your choice. Each question is worth two...

When an object with mass m = 4 k g is hung vertically on a certain light spring that obeys Hooke's law, the spring stretches 4 . 5 c m . The stored potential energy ( in J ) in this spring for this...

Suppose an object of mass m is attached to the end of a spring hanging from the ceiling. The mass is at its equilibrium position y = 0 when the mass hangs at rest. Suppose you push the mass to a...

Find the Jordan form and a Jordan basis for each matrix (a) (b) (c) (d) (e) (f) (g) -10 4 25 10 7 9 034 425 103 1 -2 1 9 7-4 444 2 2-1 2 8 2152 1411

FreeWheeler, Ltd., manufactures three bicycle models: a racing bike, a mountain bike, and a childrens model. The racing model is made of a titanium-aluminum alloy and is called the Featherweight. The...

Determine a state variable model for the circuit shown in Figure P3.22. The state variables are x(t)= i(t), x(t)= v(t), and x3(t)=v2(t). The output variable is vo(t). R v(1) R v2(1) 0 + v(t) (1) T C...

Corporation is a diversified U.S. firm that has ownership stakes in two other U.S. corporations. Specifically, DMM Corporation owns 60% of the outstanding stock of Tax Shelter.com and 10% of the...

Following graduation, you meet Mr. Big at a country club. Mr. Big is a venture capitalist who has a sizable stock portfolio concentrated in a single firm, Blue Hat. After several weeks of golfing...

A 70 year old recently retired engineer is discussing with you, over coffee, whether to gift $ 500,000 to-day to his only $500,000 today to his only daughter or invest the $ 500,000 and bequeath the...

Suppose your parents founded a wildly successful business in which they still own 90% of the outstanding stock, which is the source of most of their wealth. The basis in their stock is close to zero....

Brad, Scott, and Jake each contribute property to form BSJ Corporation. Brad contributes a building with a fair market value of $450,000 and a basis of $100,000 and receives 45% of the stock of BSJ....

The news. Find a newspaper or magazine article in which some data are reported. For the data discussed in the article, answer the same questions as for Exercises 14. Include a copy of the article...

A circular loop (radius = 14 cm) of wire is placed in a magnetic field that makes an angle of 30 with the normal to the plane of the loop. The magnitude of this field increases at a constant rate...

A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of this field varies with...

A moth at about eye level is 10 cm in front of a plane mirror; you are behind the moth, 30 cm from the mirror. What is the distance between your eyes and the apparent position of the moth's image in...

A firm has the following balance sheet: Assets Liabilities and Equity Cash $ 20,000 Accounts payable $ 20,000 Accounts receivable 155,000 Long-term debt 117,000 Inventory 111,500 Common stock ($7...

The North University System is granting scholarships for the best average of the year. The student must select one of two options analyzing the benefit of it at the time of awarding the scholarship...

A corporation has decided to replace an existing asset with a newer model. Two years ago, the existing asset originally cost $30,000 and was being depreciated under MACRS using a five-year recovery...