Question

A mass of 50 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 40 cm/s, and if there is no damping, determine the position u of the mass at any time t.

Enclose arguments of functions in parentheses. For example, sin(2x).

Assume g=9.8 ms2. Enter an exact answer.

u(t)=?

Answer #1

Conservation of energy to find amplitude of simple harmonic motion.

By finding k,angular frequency can be found out.

Solution is uploaded below.

A mass of 100 g stretches a spring 1.568 cm. If the mass is set
in motion from its equilibrium position with a downward velocity of
40 cms, and if there is no damping, determine the position u of the
mass at any time t.
Enclose arguments of functions in parentheses. For example,
sin(2x).

A mass of 100 g stretches a spring 5 cm. If the mass is set in
motion from its equilibrium position with a downward velocity of 10
cm/s, and if there is no damping, determine the position u
of the mass at any time t. (Use g = 9.8
m/s2 for the acceleration due to gravity. Let
u(t), measured positive downward, denote the displacement in meters
of the mass from its equilibrium position at time t
seconds.)
u(t) =
When does...

A mass of 3 kg stretches a spring 61.25 cm. Supposing that there
is no damping and that the mass is set in motion from 0.5 m above
its equilibrium position with a downward velocity of 2 m/s,
determine the position of the mass at any time. Find the amplitude,
the frequency, the period and the phase shift of the motion.

A mass of 8 kg stretches a spring 16 cm. The mass is acted on by
an external force of 7sin(t/4)N and moves in a medium that imparts
a viscous force of 3 N when the speed of the mass is 6 cm/s.If the
mass is set in motion from its equilibrium position with an initial
velocity of 4 cm/s, determine the position u of the mass at any
time t. Use 9.8 m/s^2 as the acceleration due to gravity....

A mass weighing 19.6 N stretches a spring 9.8 cm. The
mass is initially released from
a point 2/3 meter above the equilibrium position with a downward
velocity of 5
m/sec.
(a) Find the equation of motion.
(b)Assume that the entire spring-mass system is submerged in a
liquid that
imparts a damping force numerically equal to β (β > 0) times the
instantaneous
velocity.
Determine the value of β so that the subsequent motion is
overdamped.

A
mass weighing 3 lb stretches a spring 3 in. If the mass is pushed
upward, contracting the spring a distance of 1 in, and then set in
motion with a downward velocity of 2 ft/s, and if there is no
damping, find the position u of the mass at any time t. Determine
the frequency, period, amplitude, and phase of the motion

A
mass of 1kg stretches a spring by 32cm. The damping constant is
c=0. Exterbal vibrations create a force of F(t)= 4 sin 3t Netwons,
setting the spring in motion from its equilibrium position with
zero velocity. What is the coefficient of sin 3t of the
steady-state solution? Use g=9.8 m/s^2. Express your answe is two
decimal places.

A mass of 1 kg stretches a spring 9.8 m. The mass is acted on by
an external force of 4 cos(t) N. If the mass is set in motion from
its equilibrium position with a downward velocity of 2 m/s, find
the position of the mass at any time. Identify the transient (i.e.,
complementary) and steady state (i.e., particular) solutions. Does
the motion exhibit resonance or a beat?

A mass of 1 slug, when attached to a spring, stretches it 2 feet
and then comes to rest in the equilibrium position. Starting at t =
0, an external force equal to f(t) = 4 sin(4t) is applied to the
system. Find the equation of motion if the surrounding medium
offers a damping force that is numerically equal to 8 times the
instantaneous velocity. (Use g = 32 ft/s2 for the
acceleration due to gravity.)
What is x(t) ?...

A
mass weighing 8 pounds stretches a spring 2 feet. At t=0 the mass
is released from a point 2 feet above the equilibrium position with
a downward velocity of 4 (ft/s), determine the motion of the
mass.

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