Question

A mass of 0.520 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.780 m)cos[(18.0 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass (b) force constant for the spring N/m (c) position of the mass after it has been oscillating for one half a period (d) position of the mass one-third of a period after it has been released How can you determine the position of the object at a specific time from an expression for the position of the object at any time? m (e) time it takes the mass to get to the position x = −0.500 m after it has been released (s)

Answer #1

A mass of 0.12 kg is attached to a spring and set into
oscillation on a horizontal frictionless surface. The simple
harmonic motion of the mass is described by
x(t) = (0.42 m)cos[(14
rad/s)t].
Determine the following.
(a) amplitude of oscillation for the oscillating mass
(b) force constant for the spring
(c) position of the mass after it has been oscillating for one half
a period
(d) position of the mass one-third of a period after it has been
released...

A mass of 0.380 kg is attached to a spring and set into
oscillation on a horizontal frictionless surface. The simple
harmonic motion of the mass is described by
x(t) = (0.800 m)cos[(10.0
rad/s)t].
Determine the following.
(a) amplitude of oscillation for the oscillating mass
____m
(b) force constant for the spring
____ N/m
(c) position of the mass after it has been oscillating for one half
a period
______ m
(d) position of the mass one-sixth of a period...

A mass is attached to the end of a spring and set into
oscillation on a horizontal frictionless surface by releasing it
from a stretched position. The position of the mass at any time is
described by x = (6.6 cm)cos[2?t/(1.58
s)]. Determine the following.
(a) period of the motion
s
(b) frequency of the oscillations
Hz
(c) first time the mass is at the position x = 0
(d) first time the mass is at the site of maximum...

A mass of 1.79 kg is placed on a spring with spring constant of
280 N/m. After being pulled to its positive amplitude position and
released, the resulting simple harmonic motion has a maximum
velocity of 1.126 m/s.
(a) Calculate the angular frequency of the
oscillation. rad/s
(b) Calculate the minimum time elapsed for the mass to reach the
0.044 m position (distance from the equilibrium
position). s
(c) Calculate the velocity of the mass at the time found in part
(b). m/s

A simple harmonic oscillator consists of a block of mass 1.80 kg
attached to a spring of spring constant 360 N/m. When t = 0.520 s,
the position and velocity of the block are x = 0.200 m and v =
4.420 m/s. (a) What is the amplitude of the oscillations? What were
the (b) position and (c) velocity of the block at t = 0 s?

A mass of 187 g is attached to a spring and set into simple
harmonic motion with a period of 0.286 s. If the total energy of
the oscillating system is 6.94 J, determine the following.
(a) maximum speed of the object
m/s
(b) force constant
N/m
(c) amplitude of the motion
m

An object of mass (m = 0.8 kg) is attached to a horizontal
spring. Its position varies with time as x = (0.33
m)cos(0.2πt).
(a) Find the amplitude of its motion (in m).
(b) Find the spring constant (in N/m).
(c)Find the position (in m) at t = 0.2 s.
(d)Find the speed (in m/s) of the object at t = 0.2 s.

A mass on a spring is set oscillating by first compressing the
spring 3cm in the negative direction, then releasing the mass from
rest. The period of oscillation is 1s. Which equation(s) best
describes the position as a function of time? Select one or
more:
A. x = 3cm cos(2π t +π)
B. x = -3cm cos(2π t + 0 )
C. x = 3cm cos(2π t + π/2 )
D. x = 3cm cos(2π t - π/2 )

A 0.58 kg mass is attached to a light spring with a force
constant of 31.9 N/m and set into oscillation on a horizontal
frictionless surface. If the spring is stretched 5.0 cm and
released from rest, determine the following.
(a) maximum speed of the oscillating mass
m/s
(b) speed of the oscillating mass when the spring is compressed 1.5
cm
m/s
(c) speed of the oscillating mass as it passes the point 1.5 cm
from the equilibrium position
m/s...

A 0.68 kg mass is attached to a light spring with a force
constant of 36.9 N/m and set into oscillation on a horizontal
frictionless surface. If the spring is stretched 5.0 cm and
released from rest, determine the following.
(a) maximum speed of the oscillating mass
m/s
(b) speed of the oscillating mass when the spring is compressed 1.5
cm
m/s
(c) speed of the oscillating mass as it passes the point 1.5 cm
from the equilibrium...

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