Question

1. A mass is attached to a horizontal spring, and oscillates with a period of 1.2 s and with an amplitude of 14 cm. At t = 0 s, the mass is 14 cm to the right of the equilibrium position.

a) Write down the function for the position, velocity, and acceleration of the mass as a function of time. The only variable you should have in your expressions is time. Make sure you indicate the units for each function.

b) Plot of the position vs time and velocity vs time from 0 s to 2.4 s. On each plot, make sure you label the period, initial value and amplitude.

c) What is the distance traveled between t = 0.3 s and t = 1.6
s?

Hint: If you are not sure how to answer this problem, the graph of
position vs time from part b)

may be useful.

d) At what position (or positions) is the speed of the block two-thirds of the maximum speed?

Hint: You do not need the mass or the spring constant to solve this. Solve this problem using energy considerations, and recall that ω = ?k/m → k = mω2. You can calculate the maximum speed from the information you have.

Answer #1

A 205 g mass attached to a horizontal spring oscillates at a
frequency of 1.00 Hz . At t =0s, the mass is at x= 4.20 cm and has
vx =− 23.0 cm/s . Determine: (a) the period s (b) the angular
frequency rad/s (c) the amplitude cm (d) the phase constant rad (e)
the maximum speed cm/s (f) the maximum acceleration cm/s2 (g) the
total energy J (h) the position at t = 4.2s

A mass attached to a spring oscillates back and forth on a
horizontal frictionless surface. The velocity of the mass is
modeled by the function v = 2πfA cos(2πft) when at t = 0, x = 0.
What is the magnitude of the velocity in cm/s at the equilibrium
position for an amplitude of 4.5 cm and a frequency of 2.3 Hz?

A mass attached to a spring oscillates with a period of 1.12·s
and an amplitude of 40·cm. At time t = 0 the mass is at x = +28·cm
and is moving in the positive direction (away from equilibrium).
What is the phase constant? (degrees) Where is it at time t =
4.5·s? (cm)

A 0.200 kg mass attached to a horizontal spring is displaced
15.4 cm from rest and then released. If the mass oscillates 8.00
times in 19.3 s, what is the spring constant in the spring? 0.0344
N/m 1.36 N/m 6.78 N/m 0.0212 N/m
What is the time constant of an oscillator if its amplitude of
oscillation is decreased to 32.3% of its original value in 8.50
s?
7.52 s 15.0 s 3.76 s 1.22 s
A ball is attached to...

A particle with mass 2.61 kg oscillates horizontally at the end
of a horizontal spring. A student measures an amplitude of 0.923 m
and a duration of 129 s for 65 cycles of oscillation. Find the
frequency, ?, the speed at the equilibrium position, ?max, the
spring constant, ?, the potential energy at an endpoint, ?max, the
potential energy when the particle is located 68.5% of the
amplitude away from the equiliibrium position, ?, and the kinetic
energy, ?, and...

A 195 g mass attached to a horizontal spring oscillates at a
frequency of 2.50 Hz . At t =0s, the mass is at
x= 6.00 cm and has vx =? 40.0 cm/s .
Determine:? the phase constant, the maximum speed, the maximum
acceleration and the total energy

A mass attached to a spring oscillates with a period of 3.26 s.
If the mass starts from rest at x = 0.0410 m and time t = 0, where
is it at time t = 3.27 s?

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 ?

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