Tuning Forks in Neurology Tuning forks are used in the diagnosis of nervous affl

Question

Tuning Forks in Neurology Tuning forks are used in the diagnosis of nervous afflictions known as large-fiber polyneuropathies, which are often manifested in the form of reduced sensitivity to vibrations. Disorders that can result in this type of pathology include diabetes and nerve damage from exposure to heavy metals. The tuning fork in the figure(Figure 1) has a frequency of 135 Hz .

Part A

If the tips of the fork move with an amplitude of 1.15 mm , find their maximum speed.

Part B

Find their maximum acceleration. Give your answer as a multiple of g .

2) A 0.88-kg air cart is attached to a spring and allowed to oscillate.

Part A

If the displacement of the air cart from equilibrium is x=(10.0cm)cos[(2.00s1)t+], find the maximum kinetic energy of the cart.

Express your answer using two significant figures

Part B

Find the maximum force exerted on it by the spring.

Express your answer using two significant figures.

Thanks!

Explanation / Answer

Given that

The tuning fork has a frequency (f) =135 Hz

If the tips of the fork move with an amplitude(A) = 1.15 mm =1.15*10-3m

We know that agnular frequency (w) =2pif =2*3.14*135 =847.8rad/s

Now the maximum speed is (vmax) =Aw =(1.15*10-3m)(847.8rad/s)=0.975m/s

Their maximum acceleration is given by

amax =-Aw2 =(Aw)(w)=-(0.975m/s)(847.8rad/s) =-826.579m/s2

We can write in terms g as amax = -84.258g

2)

a)

Given that

Mass attached to the spring (m) =0.88kg

x=(10.0cm)cos[(2.00s1)t+]

A =10cm

w =2s-1

From the above equation we know that

vmax =Aw =(10cm)(2s-1) =20cm/s =0.2m/s

amax =-(aw)w =-0.4m/s2

The maximum kinetic energy is given by

KEmax= (1/2)mv2 =0.5*0.88*(0.2)2 =0.0176J

The maximum force exerted on it by the spring is

Fmax= mamax =0.88kg*(0.4) =0.352N

.

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