Question

Two springs are attached end-to-end to a green box of mass M as shown in the figure. Determine an expression that gives the period T of motion for the box attached to this combination of springs. The two individual springs have spring constants of k1 and k2, respectively.

Answer 1

The period T of a box of mass M attached to two springs with constants k1 and k2 in series is given by T = 2π sqrt(M/keq), where keq is calculated as 1/keq = 1/k1 + 1/k2.

Step-by-step explanation:

To determine an expression for the period T of motion for a box of mass M attached to two springs with spring constants k1 and k2 attached end-to-end, we need to use the concept of series spring constants and the formula for the period of a mass-spring system undergoing simple harmonic motion (SHM).

When two springs are attached in series, the equivalent spring constant keq can be found using the formula:

1/keq = 1/k1 + 1/k2

Once the equivalent spring constant is determined, the period of the mass-spring system can be found with the following equation for SHM:

T = 2π sqrt(M/keq)

Where T is the period, M is the mass of the box, and keq is the equivalent spring constant of the two springs connected in series.