22. A 2.00 kg mass attached to a spring oscillates with a period of 0.400 s and

Question

22. A 2.00 kg mass attached to a spring oscillates with a period of 0.400 s and an amplitude of 20.0 cm. Find (a) the total mechanical energy of the system; (b) the maximum speed of the mass. 23. A 50.0 kg mass attached to a spring oscillates with an amplitude of 2.00 m. The total mechanical energy of the system is 400 J. Find the position of the mass when its speed is 2.00 m/s. 25. A point on the A string of a guitar oscillates in approximately simple harmonic motion with a frequency of 220 Hz and an amplitude of 1.00 mm. Find the maxi - mum speed and acceleration of this point

Explanation / Answer

22.
a)given T=0.4s ,m=2kg

A=20cm =0.2m

T=2/=>=2/0.4 =15.7 rad/s

=(k/m)=>k=2m

k =15.72*2 =493.5N/m

E=(1/2)kA2=(1/2)*493.5*(0.2)2 =9.87J

b)Vmax =A =0.2*15.7 =3.14m/s

23.

E=(1/2)kA2=>k=2E/A2

K=2*400/22 =200J

By the law of conservation of energy,
E=KE+PE

400 =(1/2)mV2+(1/2)kx2

800 =50*22+200x2

600=200x2

x =1.732m

24.

=2f=2*220 =1382.3rad/s

Vmax=A =1*10-3*1382.3 =1.38m/s

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.