Second-order constant-coefficient differential equations can be used to model spring-mass systems.
An examination of the forces on a spring-mass system results in a differential equation of the form
where
represents the mass,
is the coefficient of the damping force,
is the spring constant, and
represents any net external forces on the system.
If
there is no damping force acting on the system, and simple harmonic motion results. If
the behavior of the system depends on whether
or
If
the system is overdamped and does not exhibit oscillatory behavior.
If
the system is critically damped. It does not exhibit oscillatory behavior, but any slight reduction in the damping would result in oscillatory behavior.
If
the system is underdamped. It exhibits oscillatory behavior, but the amplitude of the oscillations decreases over time.
If
the solution to the differential equation is the sum of a transient solution and a steady-state solution. The steady-state solution governs the long-term behavior of the system.
The charge on the capacitor in an
RLC series circuit can also be modeled with a second-order constant-coefficient differential equation of the form
where
L is the inductance,
R is the resistance,
C is the capacitance, and
is the voltage source.
Key equations
Equation of simple harmonic motion
Solution for simple harmonic motion
Alternative form of solution for SHM
Forced harmonic motion
Charge in aRLCseries circuit
A mass weighing 4 lb stretches a spring 8 in. Find the equation of motion if the spring is released from the equilibrium position with a downward velocity of 12 ft/sec. What is the period and frequency of the motion?
A mass weighing 2 lb stretches a spring 2 ft. Find the equation of motion if the spring is released from 2 in. below the equilibrium position with an upward velocity of 8 ft/sec. What is the period and frequency of the motion?
A 100-g mass stretches a spring 0.1 m. Find the equation of motion of the mass if it is released from rest from a position 20 cm below the equilibrium position. What is the frequency of this motion?
A 400-g mass stretches a spring 5 cm. Find the equation of motion of the mass if it is released from rest from a position 15 cm below the equilibrium position. What is the frequency of this motion?
A block has a mass of 9 kg and is attached to a vertical spring with a spring constant of 0.25 N/m. The block is stretched 0.75 m below its equilibrium position and released.
Find the position function
of the block.
Find the period and frequency of the vibration.
Sketch a graph of
At what time does the block first pass through the equilibrium position?
A block has a mass of 5 kg and is attached to a vertical spring with a spring constant of 20 N/m. The block is released from the equilibrium position with a downward velocity of 10 m/sec.
Find the position function
of the block.
Find the period and frequency of the vibration.
Sketch a graph of
At what time does the block first pass through the equilibrium position?
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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