Question

. A 1.50kg mass on a spring has a displacement as a function of time given by the equation: x(t) = (7.40cm)cos[(4.16s-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) at t= 1.00s, find the mass is a. the position, b. the speed, c. the acceleration d. the force on the mass

Answer 1

Answer:

Solution:

we have given the equation of motion is x(t)=8sint [where t in seconds and x in centimeter]

Position, velocity and acceleration are all based on the equation of motion.

The equation represents the position.  The first derivative gives the velocity and the 2nd derivative gives the acceleration.

x(t)=8sint

x'(t)=8cost

x"(t)=-8sint

now at time t=2pi/3,

position, x(t)=8sin(2pi/3)=4*squart(3)cm.

velocity, x'(t)=8cos(2pi/3)==4cm/s

acceleration, x"(t)==8sin(2pi/3)=-4cm/s^2

so at present the direction is in y-axis.

Answer 2

The question is looks at displacement in relation to time.

The definition of displacement

This refers to a change in the position of an object, person, or matter within a space of reference. An example would be a passenger moving from the front of the bus to the back of it.

Summary

The answers required are given summarily as follows:

A) 1.51 s

B) 26.0 N/m

C) 0.308 m/s

D) 1.92 N

E) -0.0125 m, =0.303 m/s, 0.216 m/s²

F) 0.324 N


See the attached for the step by step calculation and the link below for more exercises related to displacement:

https://brainly.com/question/8429860