A 0.500-kg mass on a spring has velocity as a

Danelle Albright

Danelle Albright

Answered question


A 0.500-kg mass on a spring has velocity as a function of time given by vx(t)=(3.60cms})sin[(4.71rads)t(π2)]. What are (a) the period; (b) the amplitude; (c) the maximum acceleration of the mass; (d) the force constant of the spring?

Answer & Explanation

Ben Owens

Ben Owens

Beginner2022-01-06Added 27 answers

Step 1
Given that the mass of the object is m=0.5kg.
The velocity of the object as a function of time given by
vx(t)=(3.6cms1)sin[(4.71rads1)tπ2] ​(1)
Since we know that the displacement in SHM is given by
x=Acos[ωtϕ] (2)
By differentiating above equation with respect to time we get the velocity of the object in SHM, so
vx(t)=Aωsin[ωtϕ] (3)
Now by comparing the equation (1) and (3), we get
Aω=3.6cms1 (4)
ω=4.7rads1 (5)
ϕ=π2rad (6)
(a) The period of SHM is given by
=1.33s (7)
Matthew Rodriguez

Matthew Rodriguez

Beginner2022-01-07Added 32 answers

Step 2
=0.76cm (8)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?