A block attached to an ideal spring of force constant (spring constant)15 N/m executes simple harmonic motion on a frictionless horizontal surface.At time t = 0 s,the block has a displacement of -0.90 m,a velocity of -0.80 m/s,and an acceleration of +2.9 m/s² .The mass of the block is closest to A)2.3 kg. B)2.6 kg. C)4.7 kg. D)9.4 kg.

Question

Quizplus · Accepted Answer

The equation for the period (T) of a mass-spring system is T=2π√(m/k), where m is the mass and k is the spring constant. The equation for the maximum displacement (A) of a mass-spring system is A=|F|max/k, where |F|max is the maximum force applied to the system.
Using the given initial conditions, we can find the amplitude A:
A = |-kx|max = |-15 N/m * (-0.90 m)| = 13.5 N
Now we can use the amplitude and period equations to find the mass:
T = 2π√(m/k)
m = k(T/2π)^2
m = (15 N/m)(1/2π)^2(2π/2.9 s)^2
m ≈ 4.7 kg
Thus, the closest answer choice is C) 4.7 kg.

A Block Attached to an Ideal Spring of Force Constant