A 1.5 kg mass on a spring has displacement as a function of time given by the eq

Question

A 1.5 kg mass on a spring has displacement as a function of time given by the equation x(t)=(7.40 cm) cos[(4.16 s^(-1) )t-2.42] Find (a) the time for one complete vibration (b) the force constant of the spring (c) the maximum speed of the mass (d) the maximum force on the mass (e) the position, speed and acceleration of the mass at t=1.00s (f) the force on the mass at that time.

what is the force on the mass at that time and (d) the maximum force on the mass (e) the position, speed and acceleration of the mass at t=1.00s (f) the force on the mass at that time.

Explanation / Answer

.The general equation for position of a spring is:
x(t) = Acos(t + )

You got
x(t) = 0.074cos(4.16t - 2.42)
so
A = 0.074 m
= 4.16 rad/s
= 2.42 rad

We know that:
T = 2 /
so
T = 2 / 4.16
T = 1.51 s < - - - - - answer A

We know that:
k = m ²
so
k = 1.5 4.16²

k = 25.96 N/m < - - - - - answer B

We know that:
Ep = k A² / 2
so
Ep = 25.96 0.074² / 2
Ep = 0.07107 J
We also know that:
Ep = Ek
so
0.07107 = 1.5 v² / 2
v = 0.308 m/s < - - - - - answer C

We know that
F = k A
so
F = 25.96 0.074
F = 1.92 N < - - - - - answer D

(f) x(t) evaluated at t=1 gives x=-0.0125 m, Vx=39.4 cm/s, a=-kx/m=-w^2x=+0.216m/s^2v <------------ ans e

(f) F=k*x=25.96*0.0125=0.3245 N >-------------------- ans f

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