A 20-kg mass is placed on a horizontal frictionless surface and then connected by two springs with spring constants k₁ = 5.0 N/m and k₂ = 3.0 N/m to walls as shown in the figure.What is the period of oscillations for the 20-kg mass if it is displaced slightly to one side? A)2.5 s B)7.0 s C)9.9 s D)14 s E)20 s

Question

Quizplus · Accepted Answer

We can find the period of oscillations using the formula:
T = 2π√(m/k_eff)
where m is the mass and k_eff is the effective spring constant.
Since the mass is connected to two springs in parallel, the effective spring constant is:
k_eff = k_1 + k_2
k_1 = 5.0 N/m and k_2 = 3.0 N/m
k_eff = 5.0 N/m + 3.0 N/m = 8.0 N/m
Substituting the values, we get:
T = 2π√(20 kg / 8.0 N/m) = 9.9 s
Therefore, the answer is C) 9.9 s.

A 20-Kg Mass Is Placed on a Horizontal Frictionless Surface