Elastic string ( S.H.M)

Classical Mechanics Level pending

A particle P of mass 1.5 kg is attached to the midpoint of a light elastic string of natural length 1.2 m and modulus of elasticity 15 N . The ends of the string are fixed to the points A and B where A is vertically above B and AB= 2.8 m . Given that P is in equilibrium, the particle is now pulled downwards a distance 0.15 m from its equilibrium position and released from rest and it moves with simple harmonic motion . T seconds after being released P is 0.1 m above its equilibrium position. Find the value of T in seconds to 3 decimal places


The answer is 0.398.

Black Bird by Black Bird , 17, Bangladesh

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1 solution

Steven Chase
Mar 17, 2021 
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import math

dt = 10.0**(-6.0)  # time step

m = 1.5   # particle mass

L0 = 0.6       # natural length of each half of string
delta = 15.0   # modulus of elasticity

yA = 2.8       # vertical position of point A
                # yB = 0

############################

# Initialize simulation

t = 0.0           # time

y = yA/2.0 - 0.15 # starting position of particle (0.15 below equilibrium)
yd = 0.0          # velocity 
ydd = 0.0         # acceleration

flag = 0          # quality flag asserts if strains negative

while y <= yA/2.0 + 0.1:  # while y below equilibrium + 0.1

    y = y + yd*dt          # numerical integration
    yd = yd + ydd*dt

    Lbot = y              # length of top and bottom half strings
    Ltop = yA - y

    strain_bot = (Lbot - L0)/L0   # strains for half strings
    strain_top = (Ltop - L0)/L0

    Fbot = -delta*strain_bot     # forces for half strings
    Ftop = delta*strain_top      # bottom string pulls down, top string pulls up

    F = Fbot + Ftop              # total force

    ydd = F/m                    # acceleration

    if (strain_bot < 0.0) or (strain_top < 0.0):  # check that strains are positive
        flag = 1

    t = t + dt

############################

# Results

print dt
print t
print flag

#>>> 
#1e-06
#0.398462999996
#0
#>>>

1 Helpful 1 Interesting 1 Brilliant 0 Confused

Upvoted!
@Steven Chase will I get the option to download all your problems and solutions ??
Please reply .

Talulah Riley - 1 week ago

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