Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

A 190 g block hangs from a spring with spring constant 9.0 N/m. At t=0s the block is 29 cm below the equilibrium point and moving upward with a speed of 116 cm/s.

What is the block's oscillation frequency?

What is the block's distance from equilibrium when the speed is 57 cm/s ?

What is the block's distance from equilibrium at t = 7.0 s ?


Sagot :

The block's oscillation frequency is 1.1 Hz.

The block's distance from equilibrium when the speed is 57 cm/s  is 14.2 cm.

The block's distance from equilibrium at t = 7.0 s  is 10.37 cm.

Oscillation frequency of the block

The oscillation frequency of the block is calculated as follows;

f = 1/2π√(k/m)

f = 1/2π √(9/0.19)

f = 1.1 Hz

Angular speed of the block

ω = 2πf

ω = 2π x 1.1

ω = 6.91 rad/s

Equation of the block's motion

x(t) = A cos(ωt + Φ)

at t = 0, phase constant is calculated as

ωX sin(Ф) = v

6.91 x 29 sin(Ф) = 116

sin(Ф) = 116/200.39

sin(Ф) = 0.579

Ф = arc sin(0.579)

Ф = 0.62 rad

Amplitude of the wave

29 = A cos(6.91 x 0  +  0.62)

29 = A cos(0.62)

29 = A(0.814)

A = 35.63 cm

Distance of the block at given speed

when the speed is 57 cm/s, the distance of the block is calculated as follows;

ωX sin(Ф) = v

(6.91)X sin(0.62) = 57

X(4.015) = 57

X = 57/4.015

X = 14.2 cm

Distance of the block at given time

x(t) = A cos(ωt + Φ)

x(7) = 35.63 cos(6.91 x 7   +  0.62)

x(7) = 10.37 cm

Learn more about oscillation frequency here: https://brainly.com/question/12950704

#SPJ1

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.