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    Mass-spring system, pendulum, oscillator frequency, sound pulses, harmonics

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    Severe Mental Disorders

    This question seems to basically be asking for your opinion, so I will try to give you a few ideas about mental disorders that you can expand on.

    Throughout history, "normal" people who do not have mental disorders have always seemed to be scared or frightened of people who do suffer from mental disorders. Very early in history, these people were thought to have an evil spirit or to be under the spell of magic. Later, these people were thought to be witches or involved with the devil. Even in modern history, they have been thrown into asylums and forgotten about. Only recently, have we understood that mental disorders have biological roots in brain malfunction and people who suffer from them are not to be blamed for this. The treatment of people with mental disorders will always depend on what the social context is like at that particular time. But in all of these cases, it seems like there is one common thread... "normal" people do not understand mental disorders and react such that they do not have to be faced with it on a day-to-day basis.

    It seems this treatment of people with mental disorders is based in several misconceptions; here are a few to get you thinking so you can come up with some more:

    People are scared of things they do not understand
    People do not understand mental disorders (biological origin) so they avoid them
    Treatment doesn't always work so that can make them more scary
    History tells us mental disorders are something unknown, powerful, and infectious (not true)
    People with mental disorders can have unpredictable behavior, this may be dangerous
    People think mental disorders are easy to control
    Popular culture often does not tell the whole story about mental disorders

    So, keep in mind that mental disorders, their origin, their effects on behavior, and the way they need to be treated are often misunderstood and you will be able to answer this question.

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    SOLUTION This solution is FREE courtesy of BrainMass!

    1. (a) At what position is the speed of a mass in a mass-spring system maximum (1) x = 0, (2) x = - A, or (3) x = +A? Why? (b) If, m = 0.250 kg, k = 100 N/m, and A = 0.10 m for such a system, what is the mass's maximum speed?

    a) When the spring is compressed or extended, it has potential energy stored in it. In the un-deformed state (i.e. when the mass is at the mean position), the PE stored is zero. As mass-spring system is an isolated one and the spring's restoring force is a conservative force, total mechanical energy of the system is conserved. The mass has maximum kinetic energy at the mean position. As the mass swings to either side of the mean position, its KE is gradually converted into the PE of the spring. At the extreme positions, the mass comes to rest momentarily (KE = 0) and the spring has maximum PE.

    As stated above, the mass has maximum KE at the mean position (x=0). Hence, its speed is maximum at x = 0.

    b) As we know, PE stored in the spring = ½ kx2

    Amplitude of oscillation A = 0.1 m

    PE at the extreme position = ½ x 100 x 0.12 = 0.5 J

    KE at the mean position = PE at the extreme position

    ½ mv2 = ½ x 0.25 x v2 = 0.5

    v2 = (0.5 x 2)/0.25 = 4 or v = 2 m/s

    2. The simple pendulum in a tall clock is 0.75 m long. What are (a) the period and (b) the frequency of this pendulum?


    a) For a simple pendulum, Period T = 2Π√(l/g) where l = length of the pendulum and g = acceleration due to gravity = 9.8 m/s2

    Hence, T = 2x3.14x√(0.75/9.8) = 1.74 sec

    b) Frequency of oscillations (i.e. no. of oscillations per sec) = 1/T = 1/1.74 = 0.57 Hz

    3. The equation of motion of a SHM oscillator is x = (0.50 m) sin(2 pie f)t, where, x is in meters and t is in seconds. If the position of the oscillator is at x = 0.25 m at t = 0.25 s, what is the frequency of the oscillator?

    a) x = 0.5sin(2Πf)t

    Substituting x = 0.25 m and t = 0.25 sec we get:

    0.25 = 0.5sin[(2Πf)0.25]

    sin[(2Πf)0.25] = 0.25/0.5 = 0.5

    (2Πf)0.25 = sin-10.5 = 30O or Π/6

    (2Πf)0.25 = Π/6 or f = 0.33 Hz

    4. Fred strikes a steel train rail with a hammer at a frequency of 2.50 Hz, and Wilma puts her ear to the rail 1 km away (a) How long after the first strike does Wilma hear the sound? (b) What is the time interval between the successive sound pulses she hears?


    a) Speed of sound in steel rail is about 5000 m/s. To cover a distance of 1000 m, the sound wave will take 1000/5000 = 0.2 sec

    b) Frequency of the sound wave = f = 2.5 Hz.

    Time period between successive sound pulses = T = 1/f = 1/2.5 = 0.4 s

    5. If the frequency of the third harmonic of the vibrating string is 600 Hz, what is the frequency of the first harmonic?

    Third harmonic has a frequency three times of the first harmonic or the fundamental frequency. If the third harmonic is 600 Hz, fundamental frequency = 600/3 = 200 Hz

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