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## Worked example 11.3: Block and two springs

Question: A block of mass is attached to two springs, as shown below, and slides over a horizontal frictionless surface. Given that the force constants of the two springs are and , find the period of oscillation of the system. Answer: Let and represent the extensions of the first and second springs, respectively. The net displacement of the mass from its equilibrium position is then given by Let and be the magnitudes of the forces exerted by the first and second springs, respectively. Since the springs (presumably) possess negligible inertia, they must exert equal and opposite forces on one another. This implies that , or Finally, if is the magnitude of the restoring force acting on the mass, then force balance implies that , or Here, is the effective force constant of the two springs. The above equations can be combined to give Thus, the problem reduces to that of a block of mass attached to a spring of effective force constant The angular frequency of oscillation is immediately given by the standard formula Hence, the period of oscillation is    Next: Worked example 11.4: Energy Up: Oscillatory motion Previous: Worked example 11.2: Block
Richard Fitzpatrick 2006-02-02