Question

Two springs are attached side by side to a box of mass as shown in the figure. The springs have force constants of 1 and 2, respectively. Determine an expression that describes the period T of the motion of the box attached to this combination of springs. Assume that the box does not rotate, so the amount of stretch or compression for each spring is the same.

Answer 1

The period T of the box attached to two side-by-side springs is described by the formula T = 2π√(m/keff), where keff is the sum of the spring constants (k1 + k2) and m is the mass of the box.

Step-by-step explanation:

To determine the expression that describes the period T of the motion of a box attached to two springs side by side, we can consider the springs' force constants k1 and k2, which are given as 1 and 2 respectively.

Since the springs are attached side by side, their effective spring constant keff is the sum of their individual constants: keff = k1 + k2. Thence, the effective force constant is keff = 1 + 2 = 3.

The period T for a simple harmonic oscillator such as this system is given by the formula: T = 2π√(m/keff), where m is the mass of the box. Replace keff with the sum of the spring constants to find the period of the box.