Question

A 0.9 kg block attached to a spring of force constant 13.1 N/m oscillates with an amplitude of 3 cm.

A) Find the maximum speed of the block. Answer in units m/s.

B) Find the speed of the block when it is 1.5 cm from the
equilibrium position. Answer in units of m/s^{.}

C) Find its acceleration at 1.5 cm from the equilibrium
position. Answer in units of m/s^{2}.

D) Find the time it takes for the block to move from x = 0 to x= 1.5cm. Answer in units of s.

Answer #1

The position of anything undergoing simple harmonic motion could be described by

x = A sin(ωt) [1]

Velocity and acceleration can be derived by taking consecutive derivatives with respect to time.

v = Aω cos(ωt) [2]

a = -Aω² sin(ωt) [3]

For a mass-spring system,

ω² = k/m [4]

i.

Since the maximum of a cosine function is 1, from [2]

v = Aω

v = A sqrt(k/m) (from [4])

v = (0.03 m) sqrt[(13.1 N/m)/(0.9 kg)]

v **= 0.114 m/s**

ii.

x = A sin(ωt) [1]

0.015 m = (0.03 m) sin(ωt)

ωt = π/6

v = Aω cos(ωt) [2]

v = (0.114 m/s) cos(π/6) (from i.)

v = **0.0987 m/s**

iii.

a = -Aω² sin(ωt) [3]

a = -xω² (from [1])

a = -x(k/m) (from [4])

a = -(0.03 m)[(13.1 N/m)/(0.9 kg)]

a = **-0.437
m/s²**

A block of mass m = 0.53 kg attached to a spring with force
constant 119 N/m is free to move on a frictionless, horizontal
surface as in the figure below. The block is released from rest
after the spring is stretched a distance A = 0.13 m. (Indicate the
direction with the sign of your answer. Assume that the positive
direction is to the right.)
The left end of a horizontal spring is attached to a vertical
wall, and...

A 0.450 kg object attached to a spring with a force constant of
8.00 N/m vibrates in simple harmonic motion with an amplitude of
12.0 cm. (Assume the position of the object is at the origin at
t = 0.)
(a) Calculate the maximum value (magnitude) of its speed and
acceleration.
___cm/s
___cm/s2
(b) Calculate the speed and acceleration when the object is 9.00 cm
from the equilibrium position.
___cm/s
___cm/s2
(c) Calculate the time interval required for the object...

A 170 g block attached to a spring with spring constant 3.0 N/m
oscillates horizontally on a frictionless table. Its velocity is 25
cm/s when x0 = -5.6 cm .
What is the amplitude of oscillation?
What is the block's maximum acceleration?
What is the block's position when the acceleration is
maximum?
What is the speed of the block when x1 = 2.6 cm ?

A 120 g block attached to a spring with spring constant 3.0 N/m
oscillates horizontally on a frictionless table. Its velocity is 17
cm/s when x0 = -4.5 cm .
What is the amplitude of oscillation?
What is the block's maximum acceleration?
What is the block's position when the acceleration is
maximum?
What is the speed of the block when x1 = 2.9 cm ?

A 100 g block attached to a spring with spring constant 2.7 N/m
oscillates horizontally on a frictionless table. Its velocity is 22
cm/s when x0 = -5.6 cm . What is the amplitude of oscillation? What
is the block's maximum acceleration? What is the block's position
when the acceleration is maximum? What is the speed of the block
when x1 = 2.9 cm ?

A 0.580-kg object attached to a spring with a force constant of
8.00 N/m vibrates in simple harmonic motion with an amplitude of
13.0 cm. (Assume the position of the object is at the origin at
t = 0.)
(a) Calculate the maximum value of its speed.
cm/s
(b) Calculate the maximum value of its acceleration.
cm/s2
(c) Calculate the value of its speed when the object is 11.00 cm
from the equilibrium position.
cm/s
(d) Calculate the value of...

A 0.560-kg object attached to a spring with a force constant of
8.00 N/m vibrates in simple harmonic motion with an amplitude of
12.6 cm. (Assume the position of the object is at the origin at
t = 0.)
(a) Calculate the maximum value of its speed.
cm/s
(b) Calculate the maximum value of its acceleration.
cm/s2
(c) Calculate the value of its speed when the object is 10.60 cm
from the equilibrium position.
cm/s
(d) Calculate the value of...

A 0.560-kg object attached to a spring with a force constant of
8.00 N/m vibrates in simple harmonic motion with an amplitude of
11.4 cm. (Assume the position of the object is at the origin at
t = 0.)
(a) Calculate the maximum value of its speed.
cm/s
(b) Calculate the maximum value of its acceleration.
cm/s2
(c) Calculate the value of its speed when the object is 9.40 cm
from the equilibrium position.
cm/s
(d) Calculate the value of...

A 200 g block attached to a spring with spring constant 2.5 N/m
oscillates horizontally on a frictionless table. Its velocity is 15
cm/s when x0 = -5.6 cm .
a. What is the amplitude of oscillation?
b. What is the block's maximum acceleration?
c. What is the block's position when the acceleration is
maximum?
d. What is the speed of the block when x1x1x_1 = 3.0 cm ?

Part A
A block of unknown mass is attached to a spring with a spring
constant of 5.50 N/m and undergoes simple harmonic motion with an
amplitude of 10.0 cm. When the block is halfway between its
equilibrium position and the end point, its speed is measured to be
28.0 cm/s.
(a) Calculate the mass of the block.
________kg
(b) Calculate the period of the motion.
________s
(c) Calculate the maximum acceleration of the block.
________m/s2
Part B
A block-spring...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 20 minutes ago

asked 29 minutes ago

asked 44 minutes ago

asked 47 minutes ago

asked 56 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago