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Oscillations of Spring Combination #8211; 1. If a spring pendulum is constructed by using two spring in series and a mass m as shown in fig. (a), the resultant spring constant of the combination is given by 1/k<sub>s</sub> = 1/k<sub>1</sub> + 1/k<sub>2</sub> = k<sub>1</sub> + k<sub>2</sub>/k<sub>1</sub>k<sub>2</sub> Hence, T = 2π√m/k<sub>s</sub> (T = 2π√m times;(k<sub>1</sub> + k<sub>2</sub>) 2. If in a spring pendulum two springs are joined in parallel arrangement as shown in fig. (b) and Fig. (c), then k<sub>p</sub> = k<sub>1</sub> + k<sub>2</sub> Hence, T = 2π√m/k<sub>1</sub> + k<sub>2</sub> These rules are applicable for horizontal motion of spring mass systems too.
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