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The Effective Force Constant of Two Springs. Two springs
Chapter 14, Problem 101CP(choose chapter or problem)
The Effective Force Constant of Two Springs. Two springs with the same unstretched length but different force constants k1 and k2 are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant keff in each of the three cases (a), (b), and (c) depicted in ?Fig. P14.92?. (The effective force constant is defined by ) (d) An object with mass ?m?, suspended from a uniform spring with a force constant k , vibrates with a frequency f1. When the spring is cut in half and the same object is suspended from one of the halves, the frequency is f2. What is the ratio f1/f2?
Questions & Answers
QUESTION:
The Effective Force Constant of Two Springs. Two springs with the same unstretched length but different force constants k1 and k2 are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant keff in each of the three cases (a), (b), and (c) depicted in ?Fig. P14.92?. (The effective force constant is defined by ) (d) An object with mass ?m?, suspended from a uniform spring with a force constant k , vibrates with a frequency f1. When the spring is cut in half and the same object is suspended from one of the halves, the frequency is f2. What is the ratio f1/f2?
ANSWER:Solution 101CP Step 1: Consider the figure a) In first case imagine the mass m moves a distance x and similarly the springs k1 and k2 moves x1 and x2 .with force f1 = -k x1 and f2=-k x2 1 2 x = x1 = x2 F =f1 + f2 The force constant is given