# Physics

An object with mass 3.0 kg is executing simple harmonic motion, attached to a spring with spring constant k =210 N/m. When the object is 0.23 m from its equilibrium position, it is moving with a speed of 0.72 m/s.
(a) Calculate the amplitude of the motion.
m

(b) Calculate the maximum speed attained by the object.
m/s

1. 👍 0
2. 👎 0
3. 👁 241
1. F = m a = -kx

if x = A cos w t
v = dx/dt = -Aw sin w t
a = d^2x/dt^2 = -A w^2 cos w t = -w^2 x

so
-m w^2 x = -k x
w^2 = k/m
w^2 = 210/3 = 70
w = sqrt(70) = 8.37

when |x| = .23 , |v| = .72
.23 = A cos 8.37 t
.72 = -A (8.37) sin 8.37 t
so
cos 8.37 t = .23/A
sin 8.37 t = .086/A

cos^2 + sin^2 = 1
.0529 + .007399 = A^2
A^2 = .060299
A = .246 m
Vmax = Aw = .246(8.37) = 2.06 m/s

check my arithmetic !!!

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### Physics

An object with mass 3.7 is attached to a spring with spring stiffness constant 270 and is executing simple harmonic motion. When the object is 2.5×10−2 from its equilibrium position, it is moving with a speed of 0.45 . what is

asked by Lori on August 30, 2012
2. ### Physics

An object with mass 5.0 kg is attached to a spring with spring stiffness constant 192 N/m and is executing simple harmonic motion. When the object is 0.35 m from its equilibrium position, it is moving with a speed of 0.02 m/s.

asked by Anonymous on March 6, 2013
3. ### Physics

An object with mass 5.0 kg is attached to a spring with spring stiffness constant 192 N/m and is executing simple harmonic motion. When the object is 0.35 m from its equilibrium position, it is moving with a speed of 0.02 m/s.

asked by Anonymous on March 5, 2013
4. ### physics

An object with mass 2.0kg is attached to a spring with spring stiffness constant 240N/m and is executing simple harmonic motion. When the object is 2.2Ã—10âˆ’2m from its equilibrium position, it is moving with a speed of

asked by Dani on November 27, 2013
5. ### Physics

An object with mass 8.2 kg is attached to a spring with spring stiffness constant 370 N/m and is executing simple harmonic motion. When the object is 0.16 m from its equilibrium position, it is moving with a speed of 0.31 m/s.

asked by Anonymous on March 5, 2013
1. ### physics

An object with mass 3.0 kg is attached to a spring with spring stiffness constant k = 300 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55

asked by Nicole on March 7, 2012
2. ### physics

An object with mass 2.3 kg is executing simple harmonic motion, attached to a spring with spring constant 280 N/m . When the object is 0.019 m from its equilibrium position, it is moving with a speed of 0.65 m/s. Calculate the

asked by Schoolgirl on January 15, 2020
3. ### phyics

Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 175 N/m. The motion of the object on spring 1 has twice the amplitude as the motion

asked by MATT on November 12, 2013
4. ### physics help!

Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 155 N/m. The motion of the object on spring 1 has twice the amplitude as the motion

asked by meagan on November 19, 2011
5. ### PHYSICS

An object is attached to an ideal spring. It undergoes a simple harmonic motion with a total energy of E = 2.2 J. The amplitude of the motion is 0.7 m and the maximum speed of the object is 0.5 m/s. Find the spring constant.

asked by Unknown on April 7, 2011

More Similar Questions