
536 S.E.2d 511 (2000)
272 Ga. 884
JONES
v.
The STATE.
No. S00A1387.
Supreme Court of Georgia.
October 10, 2000.
*512 Timothy W. Hoffman, Decatur, for appellant.
J. Tom Morgan, District Attorney, Barbara B. Conroy, Maria Murcier-Ashley, Kristin L. Wood, Assistant District Attorneys,
Thurbert E. Baker, Attorney General, Paula K. Smith, Senior Assistant Attorney General, Adam M. Hames, Assistant Attorney General, for appellee.
CARLEY, Justice.
A jury found Melvin Jones guilty of the felony murder of his three-month-old daughter while in the commission of the offense of cruelty to children. The trial court entered a judgment of conviction on the jury's verdict and sentenced Jones to life imprisonment. The trial court denied Jones' motion for new trial, and he appeals.[1]
1. Construed most favorably for the State, the evidence shows that, before the victim was born, Jones beat her mother, Tonya Andrews, in an effort to cause a miscarriage. He also used a belt or his hands to strike the three other young children in the family. Jones testified that, while Ms. Andrews was out, he grabbed the victim from her crib by one of her arms and dropped her about 15 inches above the bed, as he had done before. After Ms. Andrews returned, Jones threatened and yelled at her. When the baby began to cry, Jones went to check on her, and Ms. Andrews fell asleep. When Ms. Andrews awoke, Jones told her that the child was not breathing. Paramedics could not resuscitate the victim, who had been dead for about 30 minutes. Jones began crying and said it was his fault. The medical examiner testified that, although the victim otherwise was in good health, one of her ribs was broken within the 24 hours preceding her death, and two others were broken two to three weeks earlier. The cause of death was a subdural hematoma, resulting from a blunt trauma to the head likely occurring between 12 and 16 hours prior to death. There was also evidence of shaken baby syndrome, which probably contributed to the victim's death. The evidence is sufficient to support a finding that, while the victim was in Jones' care, he fatally struck or shook her. Carter v. State, 269 Ga. 420, 422(1), 499 S.E.2d 63 (1998). Accordingly, a rational *513 trier of fact could have found proof beyond a reasonable doubt of Jones' guilt of felony murder while in the commission of child cruelty. Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979); Johnson v. State, 269 Ga. 632, 501 S.E.2d 815 (1998); Carter v. State, supra. Compare Johnson v. State, 269 Ga. 840, 506 S.E.2d 374 (1998).
2. After Jones expressed dissatisfaction with the public defender appointed to represent him, the trial court released her but refused to appoint another attorney. Thereafter, the public defender and Jones reconciled, but Jones again became dissatisfied, and the trial court required that Jones either accept representation by the public defender or represent himself. Jones chose to act as his own attorney, but contends on appeal that he did not validly waive his right to counsel and that the trial court should have appointed a new attorney to represent him.
Jones denies that he engaged in any dilatory tactics and he relies upon the trial court's failure to establish, as suggested by Raines v. State, 242 Ga.App. 727, 729(1), 531 S.E.2d 158 (2000), that he apprehended the nature of the charges, the range of allowable punishments, potential defenses and mitigating circumstances, and any possible lesser included offenses such as voluntary or involuntary manslaughter. However, this Court has held that it is not incumbent upon the trial court to make each of these inquiries. "The record need only reflect that the accused was made aware of the dangers of self-representation and nevertheless made a knowing and intelligent waiver. [Cits.]" Wayne v. State, 269 Ga. 36, 38(2), 495 S.E.2d 34 (1998). The trial court was authorized to find that Jones set forth no justifiable basis for dissatisfaction with the public defender and, therefore, that he "was attempting to use the discharge and [appointment] of other counsel as a dilatory tactic, which was `the functional equivalent of a knowing and voluntary waiver of appointed counsel.'" Bryant v. State, 268 Ga. 616, 617(2), 491 S.E.2d 320 (1997). See also Hobson v. State, 266 Ga. 638(2), 469 S.E.2d 188 (1996). "`The essential aim of the Sixth Amendment is to guarantee effective assistance of counsel, not to guarantee a defendant preferred counsel or counsel with whom a "meaningful relationship" can be established.'" [Cits.] Battle v. State, 234 Ga.App. 143, 144(2), 505 S.E.2d 573 (1998). Furthermore, the public defender testified that she made Jones fully aware of the nature of the charge, the possible sentences, and the dangers of self-representation. According to Jones' own testimony, he completely understood that, if he rejected appointed counsel, he would have to represent himself. The trial court endeavored to convince Jones to accept the public defender, informing him and his mother about his right to counsel and the qualifications of the public defender. Under all the circumstances, we conclude that Jones knowingly and intelligently waived his right to counsel after he was made aware of the dangers of self-representation. Simpson v. State, 238 Ga.App. 109, 111-112(1), 517 S.E.2d 830 (1999).
Jones further urges that the prosecutor's failure to take a more active role invalidates the waiver of counsel. In making this contention, however, Jones erroneously assumes that he has the right to receive effective legal assistance from the prosecutor. The trial court is responsible for ensuring a valid waiver of counsel, and did so. See Wayne v. State, supra.
3. Jones urges that the trial court erred in failing to instruct on involuntary manslaughter. Throughout the trial, however, Jones took the position that he did not cause the fatal injury. See Mills v. State, 187 Ga.App. 79, 80(3), 369 S.E.2d 283 (1988). Thus, there was no evidence to support such a charge. Moreover, Jones did not request an instruction on involuntary manslaughter. A trial court does not err in failing to give, sua sponte, an instruction on a lesser included offense in the absence of a written request therefor. Gadson v. State, 264 Ga. 280, 281(2), 444 S.E.2d 305 (1994). Compare Tarvestad v. State, 261 Ga. 605, 409 S.E.2d 513 (1991) (failure to charge without request on sole defense, rather than lesser included offense).
4. Jones also contends that the trial court erred by admitting similar transaction evidence, because the State's notice of intent to introduce this evidence was untimely under *514 Uniform Superior Court Rule 31.3 and because the trial court made no specific findings in compliance with Williams v. State, 261 Ga. 640, 409 S.E.2d 649 (1991). Jones made no objection at trial on either of these grounds and, thus, has waived appellate review thereof. Murphy v. State, 270 Ga. 72, 73(2)(a), 508 S.E.2d 399 (1998); Williams v. State, 267 Ga. 308, 310(3), 477 S.E.2d 570 (1996).
Judgment affirmed.
All the Justices concur.
NOTES
[1]  The crime occurred on July 24, 1995. The grand jury returned its indictment on October 17, 1995. The jury found Jones guilty on August 22, 1996, and, on the same day, the trial court entered the judgment of conviction and sentence. Jones filed a motion for new trial on September 6, 1996, and amended it on September 9, 1999, and February 9 and 11, 2000. The trial court denied that motion on February 28, 2000, and Jones filed a notice of appeal on March 28, 2000. The case was docketed in this Court on May 4, 2000 and submitted for decision on July 3, 2000.
