High School
SAT
ACT
University
MCAT
LSAT
DAT

Vertical Springs Concept Clarifier

Related Topics

Wize University Physics Textbook (Master) > Periodic Motion: Oscillations

Vertical Springs

4 Activities

A spring with k=50 Nmk=50\ \frac{N}{m}and length 10 cm10\ cmis hanging from the ceiling (the spring is massless).

In this problem, to keep the math a bit simpler, feel free to use g=10m/s2g=10 m/s^2. (No penalty for using 9.81 if you want, though.)

a) If we attach a 50 g50\ gmass to the spring and then let it fall down, by how much does the spring stretch?
b) What is the new equilibrium position of the oscillation? (Measured from the ceiling, in centimeters.)

Let's say that, after hanging the mass, we now pull it down further by an amount equal to your answer in part (a). That is, if your answer in part (a) was 5 cm, we now pull it down by an additional 5 cm. Your answer in part (a) is now the amplitude of the simple harmonic motion for the questions below.
c) What is the lowest position of the mass now? (Measured from the ceiling, in centimeters.)
d) What is the period of oscillation?
e) If you model the displacement of the mass in the form x(t)=Acos⁡(ωt+φ)x(t)=A\cos(\omega t+\varphi), what is the phase constant?
f) When the mass passes through the center of the oscillation range, what is its speed?
g) What is the acceleration when the magnitude of the acceleration when the mass is at the top or bottom of its oscillation?
h) When the mass passes through the center of the oscillation range, what is the magnitude of its acceleration?

More Vertical Springs Questions:
A mass of 100 g is attached to a vertical spring and it is at equilibrium. The mass is lowered by 10 cm and is released to oscillate. What is the spring constant if it takes 1 s to go from the lowest position to highest position in this oscillation?
Vertical spring
The springs AA, BBand CChave the same initial length. If kA=kC=0.5kBk_A=k_C=0.5k_B,
a) Find the values of mBm_B, mCm_C.
b) Rank the period of oscillations.
Hooke's Law and Simple Harmonic Motion
A stretchy rope suspended from the ceiling is 59 cm long when a 70 N weight hangs from it, but is 80 cm long when a 205 N weight hangs from it. Determine the spring constant “k” of the rope.
Practice: Dropping putty on a spring frame
A 0.15 kg frame, when suspended from a coil spring, stretches the spring 0.070 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm (as shown). Find the maximum distance the frame moves downward from its initial position.
Simple harmonic motion: Pendulum
In two separate experiments a pendulum and a mass-spring are moved from the Earth to the moon surface where gravitational acceleration is 16\frac{1}{6}of the Earth.
a) How does the amplitude of oscillations change for each system?
b) How does the frequency of oscillations change for each system?
Simple Harmonic Motion: Mass-Spring system
The springs AA, BBand CChave the same initial length. If kA=kC=0.5kBk_A=k_C=0.5k_B,
a) Find the values of mBm_B, mCm_C. Note that mass A is 1.0 kg.
b) Rank the period of oscillations for the three masses.
Simple Harmonic Motion: Mass-Spring
A mass of 200 g200\ gis attached to a free vertical spring with k=5 Nmk=5\ \frac{N}{m} Then, it is set to oscillate with an initial downward velocity of 2 m/s2\ m/sfrom its original hanging position. Find the amplitude of this oscillation.
(Hint: first, use Newton's second law to determine the initial hanging position.)
A mass of 100gr is attached to a vertical spring and it is at equilibrium. The mass is lowered by 10cm and is released to oscillate. What is the spring constant if it takes 1s to go from the lowest position to highest position in this oscillation.
Hooke's Law and Simple Harmonic Motion
A stretchy rope suspended from the ceiling is 59 cm long when a 70 N weight hangs from it, but is 80 cm long when a 205 N weight hangs from it. Determine the spring constant “k” of the rope.
Vertical spring
The springs AA, BBand CChave the same initial length. If kA=kC=0.5kBk_A=k_C=0.5k_B,
a) Find the values of mBm_B, mCm_C.
b) Rank the period of oscillations.
New Practice Question
A mass of 200gr is attached to a free vertical spring with k=5 N/m and natural length of 20cm and is set to oscillate with an initial downward velocity of 2m/s at the moment of attachment. Find the amplitude of this oscillation.